Search results for: stability and convergence analysis

Authors: Igor Velickovski, Aleksandar Stojkov, Ivana Rajkovic

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This paper investigates drivers of shock synchronization using quarterly data for 27 European countries over the period 1999-2013 and taking into account the difference between core (‘the euro area core locomotive’) and peripheral euro area and transition countries (‘the peripheral wagons’). Results from panel error-correction models suggest that core of the euro area has not been strong magnetizer of the shock convergence of periphery and transition countries since the euro inception as a result of the offsetting effects of the various factors that affected the shock convergence process. These findings challenge the endogeneity hypothesis in the optimum currency area framework and rather support the specialisation paradigm which is concerning evidence for the future stability of the euro area.

Keywords: dynamic panel models, shock synchronisation, trade, optimum currency area

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Authors: Saul A. Torres Z., Eduardo Liceaga C., Alfredo Arias M.

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We seek to develop a UAV for agricultural spraying at a maximum altitude of 5000 meters above sea level, with a payload of 100 liters of fumigant. For the developing the aerodynamic design of the aircraft is using computational tools such as the "Vortex Lattice Athena" software, "MATLAB", "ANSYS FLUENT", "XFoil" package among others. Also methods are being used structured programming, exhaustive analysis of optimization methods and search. The results have a very low margin of error, and the multi-objective problems can be helpful for future developments. Also we developed method for Stability Analysis (Lateral-Directional and Longitudinal).

Keywords: aerodynamics design, optimization, algorithm genetic, multi-objective problem, longitudinal stability, lateral-directional stability

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Authors: Omenogor, Happy Dumbi

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This paper examines the areas of convergence and divergence between English and Ųkwųanį (a language in Nigeria) vowel systems with particular emphasis on the front vowels. It specifies areas of difficulty for the average Ųkwųanį users of English and Ųkwųanį L1 users of English as a second language. The paper explains the nature of contrastive analysis, the geographical locations where Ųkwųanį is spoken as mother tongue as well as English and Ųkwųanį front vowels. The principles of establishing phonemes, minimal pairs in Ųkwųanį as well as the vowel charts in both languages are among the issues highlighted in this paper.

Keywords: convergence, divergence, English, Ukwųanį

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Authors: Anuar Ishak

Abstract:

The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, shrinking sheet, stability analysis

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Authors: Mubarak Alhajri

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This paper addresses certain inherent limitations of local priority hysteresis switching logic. Our main result establishes that under persistent excitation assumption, it is possible to relax constraints requiring strict positivity of local priority and hysteresis switching constants. Relaxing these constraints allows the adaptive system to reach optimality which implies the performance improvement. The unconstrained local priority hysteresis switching logic is examined and conditions for global convergence are derived.

Keywords: adaptive control, convergence, hysteresis constant, hysteresis switching

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Authors: Djilani Kobibi Youcef Islam, Hadjeri Samir, Djehaf Mohamed Abdeldjalil

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The Flexible AC Transmission System (FACTS) technology is a new advanced solution that increases the reliability and provides more flexibility, controllability, and stability of a power system. The Unified Power Flow Controller (UPFC), as the most versatile FACTS device for regulating power flow, is able to control respectively transmission line real power, reactive power, and node voltage. The main purpose of this paper is to analyze the effect of the UPFC on the load flow, the power losses, and the voltage stability using NEPLAN software modules, Newton-Raphson load flow is used for the power flow analysis and the modal analysis is used for the study of the voltage stability. The simulation was carried out on the IEEE 14-bus test system.

Keywords: FACTS, load flow, modal analysis, UPFC, voltage stability

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Authors: M. Macchiaroli, L. Dolores, V. Pellecchia

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With the recent Resolution n. 580/2019/R/idr, the Italian Regulatory Authority for Energy, Networks, and Environment (ARERA) for the Urban Water Management has introduced, for water managements characterized by persistent critical issues regarding the planning and organization of the service and the implementation of the necessary interventions for the improvement of infrastructures and management quality, a new mechanism for determining tariffs: the regulatory scheme of Convergence. The aim of this regulatory scheme is the overcoming of the Water Service Divided in order to improve the stability of the local institutional structures, technical quality, contractual quality, as well as in order to guarantee transparency elements for Users of the Service. Convergence scheme presupposes the identification of the cost items to be considered in the tariff in parametric terms, distinguishing three possible cases according to the type of historical data available to the Manager. The study, in particular, focuses on operations that have neither data on tariff revenues nor data on operating costs. In this case, the Manager's Constraint on Revenues (VRG) is estimated on the basis of a reference benchmark and becomes the starting point for defining the structure of the tariff classes, in compliance with the TICSI provisions (Integrated Text for tariff classes, ARERA's Resolution n. 665/2017/R/idr). The proposed model implements the recent studies on optimization models for the definition of tariff classes in compliance with the constraints dictated by TICSI in the application of the Convergence mechanism, proposing itself as a support tool for the Managers and the local water regulatory Authority in the decision-making process.

Keywords: decision-making process, economic evaluation of projects, optimizing tools, urban water management, water tariff

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Authors: Hudson Akewe

Abstract:

In this study, we introduce a modified Jungck (Dual Jungck) iterative scheme and use the scheme to approximate the unique common fixed point of a pair of generalized contractive-like operators in a Banach space. The iterative scheme is also shown to be stable with respect to the maps (S,T). An example is taken to justify the convergence of the scheme. Our result is a generalization and improvement of several results in the literature on single map T.

Keywords: generalized contractive-like operators, modified Jungck iterative scheme, stability results, weakly compatible maps, unique common fixed point

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Authors: Farangiz Davranbekova

Abstract:

Subject: The study explores the impact of Over-the-Top services in the sports rights market, focusing on football games. This impact is analysed in the big five European football markets. The research entails how the pay-TV market is combating the disruptors' entry, how the fans are adjusting to these changes and how leagues and football clubs are orienting in the transitional period of more choice. Aims and methods: The research aims to offer a general overview of the impact of OTT players in the football rights market. A theoretical framework of Jenkins’ five layers of convergence is implemented to analyse the transition the sports rights market is witnessing from various angles. The empirical analysis consists of secondary research data as and seven expert interviews from three different clusters. The findings are bound by the combination of the two methods offering general statements. Findings: The combined secondary data as well as expert interviews, conducted on five layers of convergence found: 1. Technological convergence presents that football content is accessible through various devices with innovative digital features, unlike the traditional TV set box. 2. Social convergence demonstrates that football fans multitask using various devices on social media when watching the games. These activities are complementary to traditional TV viewing. 3. Cultural convergence points that football fans have a new layer of fan engagement with leagues, clubs and other fans using social media. Additionally, production and consumption lines are blurred. 4. Economic convergence finds that content distribution is diversifying and/or eroding. Consumers now have more choices, albeit this can be harmful to them. Entry barriers are decreased, and bigger clubs feel more powerful. 5. Global convergence shows that football fans are engaging with not only local fans but with fans around the world that social media sites enable. Recommendation: A study on smaller markets such as Belgium or the Netherlands would benefit the study on the impact of OTT. Additionally, examination of other sports will shed light on this matter. Lastly, once the direct-to-consumer model is fully taken off in Europe, it will be of importance to examine the impact of such transformation in the market.

Keywords: sports rights, OTT, pay TV, football

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Authors: Mojtaba Hakimi-Moghaddam

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Routh-Hurwitz stability criterion is a powerful approach to determine stability of linear time invariant systems. On the other hand, applying this criterion to characteristic equation of a system, whose stability or marginal stability can be determined. Although the command roots (.) of MATLAB software can be easily used to determine the roots of a polynomial, the characteristic equation of closed loop system usually includes parameters, so software cannot handle it; however, Routh-Hurwitz stability criterion results the region of parameter changes where the stability is guaranteed. Moreover, this criterion has been extended to characterize the stability of interval polynomials as well as fractional-order polynomials. Furthermore, it can help us to design stable and minimum-phase controllers. In this paper, theory and application of this criterion will be reviewed. Also, several illustrative examples are given.

Keywords: Hurwitz polynomials, Routh-Hurwitz stability criterion, continued fraction expansion, pure imaginary roots

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Authors: Ali Atashbar Orang, Carlo Massimo Casciola

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A novel numerical approach for the steady incompressible turbulent flows is presented in this paper. The artificial compressibility method (ACM) is applied to the Reynolds Averaged Navier-Stokes (RANS) equations. A new Characteristic-Based Turbulent (CBT) scheme is developed for the convective fluxes. The well-known Spalart–Allmaras turbulence model is employed to check the effectiveness of this new scheme. Comparing the proposed scheme with previous studies, it is found that the present CBT scheme demonstrates accurate results, high stability and faster convergence. In addition, the local time stepping and implicit residual smoothing are applied as the convergence acceleration techniques. The turbulent flows past a backward facing step, circular cylinder, and NACA0012 hydrofoil are studied as benchmarks. Results compare favorably with those of other available schemes.

Keywords: incompressible turbulent flow, method of characteristics, finite volume, Spalart–Allmaras turbulence model

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Authors: P. Singh, S. Mittal

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Stability of slope in Chamoli Distt. near River Alaknanda in Uttarakhand is essential to safeguard the infrastructure of the slope where a dam is proposed to be built near this slope. Every year the areas near the slope have been facing severe landslides (small or big) due to intensive precipitation inflicting substantial damages as per Geological Survey of India records. The stability analysis of the slope under static and pseudo static conditions are presented in this study by using FEM software PHASE2. As per the earthquake zonation map of India, the slope is found in zone V, and hence, pseudo static stability of slope has been performed considering pseudo static analysis. For analysing the slope Mohr-Coulomb shear strength criteria is adopted for soil material and self-drilling anchors are modelled as bolts with parameters like modulus of elasticity, diameter of anchors and peak pull-out resistance of the anchors with the soil present there. The slope is found to be unstable under pseudo static conditions with computed factor of safety= 0.93. Stability is provided to the slope by using Self Drilling Anchors (SDA) which gives factor of safety= 1.15 under pseudo static condition.

Keywords: FEM, pseudo static, self-drilling anchors, slope stability

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Authors: Boualem Chetti

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The dynamic characteristics of a three-lobe journal bearing lubricated with micropolar fluids are determined by the linear stability theory. Lubricating oil containing additives and contaminants is modeled as micropolar fluid. The modified Reynolds equation is obtained using the micropolar lubrication theory and the finite difference technique has been used to solve it. The dynamic characteristics in terms of stiffness, damping coefficients, the critical mass and whirl ratio are determined for various values of size of material characteristic length and the coupling number. The computed results show compared with Newtonian fluids, that micropolar fluid exhibits better stability.

Keywords: three-lobe bearings, micropolar fluid, dynamic characteristics, stability analysis

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Authors: Saleh Maina

Abstract:

There is an on-going debate among intellectuals and scholars of international relations and world politics over the direction which the world is heading particularly in the current era of globalization. On the one hand are adherents to the convergence thesis which is premised on the assumption that global social order is tending toward universalism which could translate into the possible end of the classical state system and the unification of world societies under a single and common ideological dispensation. The convergence thesis is hinged on the globalization process which is gradually reducing world societies into a 'global village'. On the other hand are intellectuals who hold the view that despite advances made in communication technology which appear to threaten the survival of the classical state system. Invariance, as expressed in the survival of the existing state system and the diverse social traditions in world societies, remain a realistic possibility contrary to the conclusions of the convergence thesis. The invariance thesis has been advanced by scholars like Samuel P. Huntington whose work on clash of civilizations suggests that world peace can only be sustained through the co-habitation of diverse civilizations across the world. The purpose of this paper is to examine both sides of the debate with the aim of making a realistic assessment on where world societies are headed, between convergence and invariance. Using the realist theory of international relations as our theoretical premise the paper argues that while there is sufficient ground to predict the future direction of world societies as headed towards some form of convergence, invariance as expressed in the co-existence of diverse civilizations will for a long time remain a major feature of the international system.

Keywords: convergence, invariance, clash of civilization, classical state system, universalism

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Authors: Alemayehu Geremew Geremew

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We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.

Keywords: common fixed point, Mann iteration, multivalued mapping, weak convergence

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Authors: Jignesh Patel, Satish K. Joshi

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This paper presents the literature review on the works done so far in the area of stability of power system with high penetration of Wind Power with other conventional power sources. Out of many problems, the voltage and frequency stability is of prime concern as it is directly related with the stable operation of power system. In this paper, different aspects of stability of power system, particularly voltage and frequency, Optimization of FACTS-Energy Storage devices is discussed.

Keywords: small singal stability, voltage stability, frequency stability, LVRT, wind power, FACTS

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Authors: Roman Klas, František Pochylý, Pavel Rudolf

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This paper is focused on the CFD simulation of the radiaxial pump (i.e. mixed flow pump) with the aim to detect the reasons of Y-Q characteristic instability. The main reasons of pressure pulsations were detected by means of the analysis of velocity and pressure fields within the pump combined with the theoretical approach. Consequently, the modifications of spiral case and pump suction area were made based on the knowledge of flow conditions and the shape of dissipation function. The primary design of pump geometry was created as the base model serving for the comparison of individual modification influences. The basic experimental data are available for this geometry. This approach replaced the more complicated and with respect to convergence of all computational tasks more difficult calculation for the compressible liquid flow. The modification of primary pump consisted in inserting the three fins types. Subsequently, the evaluation of pressure pulsations, specific energy curves and visualization of velocity fields were chosen as the criterion for successful design.

Keywords: CFD, radiaxial pump, spiral case, stability

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: Reza Mohammadi

Abstract:

Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Sabri Arik

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In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and Homeomorphic mapping theorem, we derive some new types of sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slopebounded activation functions. An important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties symmetric matrices associated with the uncertainty sets of network parameters. The obtained results are shown to be generalization of some of the previously published corresponding results. Some comparative numerical examples are also constructed to compare our results with some closely related existing literature results.

Keywords: neural networks, delayed systems, lyapunov functionals, stability analysis

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Authors: Salah Al-Din I. Badran, Samad Ahmadi, Dylan Menzies, Ismail Shahin

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This paper describes a new efficient blind source separation method; in this method we use a non-uniform filter bank and a new structure with different sub-bands. This method provides a reduced permutation and increased convergence speed comparing to the full-band algorithm. Recently, some structures have been suggested to deal with two problems: reducing permutation and increasing the speed of convergence of the adaptive algorithm for correlated input signals. The permutation problem is avoided with the use of adaptive filters of orders less than the full-band adaptive filter, which operate at a sampling rate lower than the sampling rate of the input signal. The decomposed signals by analysis bank filter are less correlated in each sub-band than the input signal at full-band, and can promote better rates of convergence.

Keywords: Blind source separation, estimates, full-band, mixtures, sub-band

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The main purpose of this paper is to present the Modified Newmark Method of buckling analysis frame considering the effect of the axial load. The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. In this method, stiffness matrix of the structure is considered to be constant. The most important advantage of such a method is that it obtains both upper and lower critical loads. The advanced of the present method is fast convergence, ability to use computer simulations, and ability to model structures with semi-rigid support conditions using linear and rotational spring.

Keywords: buckling, stability, frame, modified newmark method

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Authors: Arbolino Roberta, Boffardi Raffaele

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Achieving the highest effectiveness for the National Plans for Recovery and Resilience (NPRR) while strengthening the objectives of cohesion and reduction of intra-EU unbalances is only possible by means of strategic, coordinated, and coherent policy planning. Therefore, the present research aims at assessing and quantifying the potential impact of NPRRs across the twenty-seven European Member States in terms of economic convergence, considering disaggregated data on industrial, construction, and service sectors. The first step of the research involves a performance analysis of the main macroeconomic indicators describing the trends of twenty-seven EU economies before the pandemic outbreak. Subsequently, in order to define the potential effect of the resources allocated, we perform an impact analysis of previous similar EU investment policies, estimating national-level sectoral elasticity associated with the expenditure of the 2007-2013 and 2014-2020 Cohesion programmes funds. These coefficients are then exploited to construct adjustment scenarios. Finally, convergence analysis is performed on the data used for constructing scenarios in order to understand whether the expenditure of funds might be useful to foster economic convergence besides driving recovery. The results of our analysis show that the allocation of resources largely mirrors the aims of the policy framework underlying the NPRR, thus reporting the largest investments in both those sectors most affected by the economic shock (services) and those considered fundamental for the digital and green transition. Notwithstanding an overall positive effect, large differences exist among European countries, while no convergence process seems to be activated or fostered by these interventions.

Keywords: NPRR, policy evaluation, cohesion policy, scenario Nalsysi

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Authors: Safia Hocine, Zina Benouaret, Djamil A¨ıssani

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In this paper, we study the performance of the strong stability method of the univariate classical risk model. We interest to the stability bounds established using two approaches. The first based on the strong stability method developed for a general Markov chains. The second approach based on the regenerative processes theory . By adopting an algorithmic procedure, we study the performance of the stability method in the case of exponential distribution claim amounts. After presenting numerically and graphically the stability bounds, an interpretation and comparison of the results have been done.

Keywords: Marcov chain, regenerative process, risk model, ruin probability, strong stability

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Authors: Oludamilare Bode Adewuyi, Yanxia Sun, Isaiah Gbadegesin Adebayo

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Voltage stability analysis is crucial to the reliable and economic operation of power systems. The power system of developing nations is more susceptible to failures due to the continuously increasing load demand, which is not matched with generation increase and efficient transmission infrastructures. Thus, most power systems are heavily stressed, and the planning of extra generation from distributed generation sources needs to be efficiently done so as to ensure the security of the power system. Some voltage stability index-based approach for DG siting has been reported in the literature. However, most of the existing voltage stability indices, though sufficient, are found to be inaccurate, especially for overloaded power systems. In this paper, the performance of a relatively different approach using a line voltage stability margin indicator, which has proven to have better accuracy, has been presented and compared with a conventional line voltage stability index for DG siting using the Nigerian 28 bus system. Critical boundary index (CBI) for voltage stability margin estimation was deployed to identify suitable locations for DG placement, and the performance was compared with DG placement using the Novel Line Stability Index (NLSI) approach. From the simulation results, both CBI and NLSI agreed greatly on suitable locations for DG on the test system; while CBI identified bus 18 as the most suitable at system overload, NLSI identified bus 8 to be the most suitable. Considering the effect of the DG placement at the selected buses on the voltage magnitude profile, the result shows that the DG placed on bus 18 identified by CBI improved the performance of the power system better.

Keywords: voltage stability analysis, voltage collapse, voltage stability index, distributed generation

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Authors: Abdelhak Soudani

Abstract:

Using the limit equilibrium method in geotechnical field is very important for large projects. This work contributes to the understanding and analysis of the building unstable slopes by the technique of soil nailed with the used of software called GEO-SLOPE calculation based on limit equilibrium method. To achieve our objective, we began a review of the literature on landslides, and techniques of slope stability. Then, we presented a real case slope likely to slip through the realization of the EastWest Highway (M5 stretch between Khemis Miliana and Hoceinia). We also process the application of reinforcement technique nailed soil. The analysis is followed by a parametric study, which shows the impact of parameters given or chosen on various outcomes. Another method of reinforcement (use of micro-piles) has been suggested for improving the stability of the slope

Keywords: slope stability, strengthening, slip, soil nail, GEO-SLOPE

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Authors: Aram Yakoby, Yossef H. Hatzor, Shmulik Pinkert

Abstract:

This work presents an applied engineering method for evaluating the stability of underground openings under conditions of uncertainty. The developed method is demonstrated by a comprehensive parametric study on a case of large-diameter vertical borehole stability analysis, with uncertainties regarding the in-situ stress distribution. To this aim, a safety factor analysis is performed for the stability of both supported and unsupported boreholes. In the analysis, we used analytic geomechanical calculations and advanced numerical modeling to evaluate the estimated stress field. In addition, the work presents the development of a boundary condition for the numerical model that fits the nature of the problem and yields excellent accuracy. The borehole stability analysis is studied in terms of (1) the stress ratio in the vertical and horizontal directions, (2) the mechanical properties and geometry of the support system, and (3) the parametric sensitivity. The method's results are studied in light of a real case study of an underground waste disposal site. The conclusions of this study focus on the developed method for capturing the parametric uncertainty, the definition of critical geological depths, the criteria for implementing structural support, and the effectiveness of further in-situ investigations.

Keywords: borehole stability, in-situ stress, parametric study, factor of safety

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Authors: Mohamed Fredj, Abdallah Hafsaoui, Radouane Nakache

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The study of the stability of the mining works in rock masses fractured is the major concern of the operating engineer. For geotechnical works in mines and quarries, it there is not today's general methodology for analysis and the quantification of the risks relating to the dangers inherent in these concrete types (falling boulders, landslides, etc.). The reasons for this are uncertainty, which weighs on available data or lack of knowledge of the values of the parameters required for this analysis type. Stability calculations must be based on reliable knowledge of the distribution of discontinuities that dissect the Rocky massif and the resistance to shear of the intact rock and discontinuities. This study is aimed to study the stability of slope of mine (Kef Sennoun - Tebessa, Algeria). The problem is analyzed using a numerical model based on the finite elements (software Plaxis 3D).

Keywords: stability, discontinuities, finite elements, rock mass, open-pit mine

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Authors: Reza Mohammadi

Abstract:

Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Muhammad A. Alsubaie, Mubarak K. H. Alhajri, Tarek S. Altowaim

Abstract:

A repetitive controller designed to accommodate periodic disturbances via state feedback is discussed. Periodic disturbances can be represented by a time delay model in a positive feedback loop acting on system output. A direct use of the small gain theorem solves the periodic disturbances problem via 1) isolating the delay model, 2) finding the overall system representation around the delay model and 3) designing a feedback controller that assures overall system stability and tracking error convergence. This paper addresses uncertainty conditions for the repetitive controller designed in state feedback in either past error feedforward or current error feedback using singular values. The uncertainty investigation is based on the overall system found and the stability condition associated with it; depending on the scheme used, to set an upper/lower limit weighting parameter. This creates a region that should not be exceeded in selecting the weighting parameter which in turns assures performance improvement against system uncertainty. Repetitive control problem can be described in lifted form. This allows the usage of singular values principle in setting the range for the weighting parameter selection. The Simulation results obtained show a tracking error convergence against dynamic system perturbation if the weighting parameter chosen is within the range obtained. Simulation results also show the advantage of weighting parameter usage compared to the case where it is omitted.

Keywords: model mismatch, repetitive control, singular values, state feedback

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