Search results for: linear matrix inequality (LMI)

Authors: Chivon Choeung, Heng Tang, Panha Soth, Vichet Huy

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This paper presents a robust control strategy for a single-phase DC-AC inverter with an output LC-filter. An all-pass filter is utilized to create an artificial β-signal so that the proposed controller can be simply used in dq-synchronous frame. The proposed robust controller utilizes a state feedback control with integral action in the dq-synchronous frame. A linear matrix inequality-based optimization scheme is used to determine stabilizing gains of the controllers to maximize the convergence rate to steady state in the presence of uncertainties. The uncertainties of the system are described as the potential variation range of the inductance and resistance in the LC-filter.

Keywords: single-phase inverter, linear matrix inequality, robust control, all-pass filter

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control

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Authors: Sofiane Bououden, Ilyes Boulkaibet

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In this paper, a robust model predictive controller (RMPC) for uncertain nonlinear system under actuator saturation is designed to control a DC-DC buck converter in PV pumping application, where this system is subject to actuator saturation and parameter uncertainties. The considered nonlinear system contains a linear constant part perturbed by an additive state-dependent nonlinear term. Based on the saturating actuator property, an appropriate linear feedback control law is constructed and used to minimize an infinite horizon cost function within the framework of linear matrix inequalities. The proposed approach has successfully provided a solution to the optimization problem that can stabilize the nonlinear plants. Furthermore, sufficient conditions for the existence of the proposed controller guarantee the robust stability of the system in the presence of polytypic uncertainties. In addition, the simulation results have demonstrated the efficiency of the proposed control scheme.

Keywords: PV pumping system, DC-DC buck converter, robust model predictive controller, nonlinear system, actuator saturation, linear matrix inequality

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Authors: Iyai Davies, Olivier L. C. Haas

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In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.

Keywords: infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability

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Authors: Jin Liang, Guanghua Shi

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In this paper, we are concerned with the further refinements of the Heinz operator inequalities in Hilbert spaces. Our purpose is to derive several new Heinz-type operator inequalities. First, with the help of the Taylor series of some hyperbolic functions, we obtain some refinements of the ordering relations among Heinz means defined by Bhatia with different parameters, which would be more suitable in obtaining the corresponding operator inequalities. Second, we present some generalizations of Heinz operator inequalities. Finally, we give a matrix version of the Heinz inequality for the Hilbert-Schmidt norm.

Keywords: Hilbert space, means inequality, norm inequality, positive linear operator

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Authors: Hisham M. Soliman, Hassan Yousef

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This manuscript presents new results on design saturated power system stabilizers (PSS) to assign system poles within a desired region for achieving good dynamic performance. The regional pole placement is accomplished against model uncertainties caused by different load conditions. The design is based on a sufficient condition in the form of linear matrix inequalities (LMI) which forces the saturated nonlinear controller to lie within the linear zone. The controller effectiveness is demonstrated on a single machine infinite bus system.

Keywords: power system stabilizer, saturated control, robust control, regional pole placement, linear matrix inequality (LMI)

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Authors: R. S. Sheu, H. Usman, M. S. Lawal

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Takagi-Sugeno (T-S) fuzzy model based control of a load frequency deviation in a single machine with limit nonlinearity on power coefficient is presented in the paper. Two T-S fuzzy rules with only rotor angle variable as input in the premise part, and linear state space models in the consequent part involving characteristic matrices determined from limits set on the power coefficient constant are formulated, state feedback control gains for closed loop control was determined from the formulated Linear Matrix Inequality (LMI) with eigenvalue optimization scheme for asymptotic and exponential stability (speed of esponse). Numerical evaluation of the closed loop object was carried out in Matlab. Simulation results generated of both the open and closed loop system showed the effectiveness of the control scheme in maintaining load frequency stability.

Keywords: T-S fuzzy model, state feedback control, linear matrix inequality (LMI), frequency deviation control

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Authors: S. H. Lee, M. J. Park, O. M. Kwon

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In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of this systems are obtained by solving a set of Linear Matrix Inequalities(LMIs). One numerical example is included to show the effectiveness of the proposed criteria.

Keywords: multi-agent, linear matrix inequalities (LMIs), kronecker product, sampled-data, Lyapunov method

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Authors: N. Chayaopas, W. Assawinchaichote

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In order to maximize energy capturing from wind energy, controlling the doubly fed induction generator to have optimal power from the wind, generator speed and output electrical power control in wind energy system have a great importance due to the nonlinear behavior of wind velocities. In this paper purposes the design of a control scheme is developed for power control of wind energy system via H∞ fuzzy integral controller. Firstly, the nonlinear system is represented in term of a TS fuzzy control design via linear matrix inequality approach to find the optimal controller to have an H∞ performance are derived. The proposed control method extract the maximum energy from the wind and overcome the nonlinearity and disturbances problems of wind energy system which give good tracking performance and high efficiency power output of the DFIG.

Keywords: doubly fed induction generator, H-infinity fuzzy integral control, linear matrix inequality, wind energy system

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Authors: Yamin Sayyari

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In this paper, we generalized the Jensen's inequality for m-convex functions and also we present a correction of Jensen's inequality which is a better than the generalization of this inequality for m-convex functions. Finally, we have found new lower and new upper bounds for Jensen's discrete inequality.

Keywords: Jensen's inequality, m-convex function, Convex function, Inequality

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Authors: Claude Tadonki

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We address the issues related to the computation of the covariance matrix. This matrix is likely to be ill conditioned following its canonical expression, thus consequently raises serious numerical issues. The underlying linear system, which therefore should be solved by means of iterative approaches, becomes computationally challenging. A huge number of iterations is expected in order to reach an acceptable level of convergence, necessary to meet the required accuracy of the computation. In addition, this linear system needs to be solved at each iteration following the general form of the covariance matrix. Putting all together, its comes that we need to compute as fast as possible the associated matrix-vector product. This is our purpose in the work, where we consider and discuss skillful formulations of the problem, then propose a parallel implementation of the matrix-vector product involved. Numerical and performance oriented discussions are provided based on experimental evaluations.

Keywords: covariance-matrix, multicore, numerical computing, parallel computing

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Authors: Adel Mohsen

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A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner.

Keywords: Broyden's updates, matrix inverse, inverse factorization, solution of linear algebraic equations, ill-conditioned matrices, preconditioning

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Authors: Alfredo Reyes-Salazar, Mario D. Llanes-Tizoc, Eden Bojorquez, Federico Valenzuela-Beltran, Juan Bojorquez, Jose R. Gaxiola-Camacho, Achintya Haldar

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Seismic analysis of steel buildings is usually based on the use of the concentrated mass (ML) matrix and the Rayleigh damping matrix (C). Similarly, the initial stiffness matrix (KO) and the first two modes associated with lateral vibrations are commonly used to develop matrix C. The evaluation of the accuracy of these practices for the particular case of steel buildings with moment-resisting steel frames constitutes the main objective of this research. For this, the non-linear seismic responses of three models of steel frames, representing low-, medium- and high-rise steel buildings, are considered. Results indicate that if the ML matrix is used, shears and bending moments in columns are underestimated by up to 30% and 65%, respectively when compared to the corresponding results obtained with the consistent mass matrix (MC). It is also shown that if KO is used in C instead of the tangent stiffness matrix (Kt), axial loads in columns are underestimated by up to 80%. It is concluded that the consistent mass matrix should be used in the structural modelling of moment-resisting steel frames and that the tangent stiffness matrix should be used to develop the Rayleigh damping matrix.

Keywords: moment-resisting steel frames, consistent and concentrated mass matrices, non-linear seismic response, Rayleigh damping

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Authors: Qiong Huang, Satish Chand

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This paper uses a primary data from 670 Chinese manufacturing firms, together with the newly introduced regressionbased inequality decomposition method, to study the effect of openness on wage inequality. We find that openness leads to a positive industry wage premium, but its contribution to firm-level wage inequality is relatively small, only 4.69%. The major contributor to wage inequality is human capital, which could explain 14.3% of wage inequality across sample firms.  

Keywords: openness, human capital, wage inequality, decomposition, China

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Authors: Wookyong Kwon, Sangmoon Lee

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In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method.

Keywords: model predictive control, sampled-data control, linear parameter varying systems, LPV

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Authors: Sungik Kang, Ja-Hoon Koo

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Globally, urban environments have become unequal, and cities have been segmented by income class. It is predicted that urban inequality has arisen by urban redevelopment and reconstruction projects that improve the urban environment and innovate cities. This study aims to analyze the occurrence and characteristics of urban inequality by using the housing price and sale price and demonstrating the correlation with the urban redevelopment project. This study measures 14 years of urban inequality index for 25 autonomous districts in Seoul and analyzes the correlation between urban inequality with urban redevelopment projects. As a conclusion of this study, first, the urban inequality index of Seoul has been continuously rising since 2015. Trends from 2006 to 2019 have been in U-curved shape in between 2015. In 2019, Seoul's urban inequality index was 0.420, a level similar to that of the 2007 financial crisis. Second, the correlation between urban redevelopment and urban inequality was not statistically significant. Therefore, we judged that urban redevelopment's scale or project structure has nothing with urban inequality. Third, while district designation of urban reconstruction temporarily alleviates urban inequality, the completion of the project increases urban inequality. When designating a district, urban inequality is likely to decrease due to decreased outdated housing transactions. However, the correlation with urban inequality increases as expensive houses has been placed after project completion.

Keywords: urban inequality, urban redevelopment projects, urban reconstruction projects, housing price inequality, panel analysis

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Authors: Maja Andrić, Josip Pečarić

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Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities.

Keywords: Opial's inequality, Jensen's inequality, integral inequality, discrete inequality

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: J. P. P. Andrade, V. A. F. Campos

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This work presents an application of Linear Matrix Inequalities (LMI) for the robust control of an F-16 aircraft through an algorithm ensuring the damping factor to the closed loop system. The results show that the zero and gain settings are sufficient to ensure robust performance and stability with respect to various operating points. The technique used is the pole placement, which aims to put the system in closed loop poles in a specific region of the complex plane. Test results using a dynamic model of the F-16 aircraft are presented and discussed.

Keywords: F-16 aircraft, linear matrix inequalities, pole placement, robust control

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Authors: Mahmoud Salari

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Corruption and gender inequality are the main topics of interest for both economists and policymakers. This study develops various static and dynamic estimation models to examine the impact of gender inequality in politics and the labor market on corruption using data of 170 countries from 1998 to 2014. This study uses two most reliable corruption indexes, including Corruption Perceptions Index (CPI) and Corruption Control (CC), to evaluate corruption levels across countries. The results indicate that gender inequality in politics has a strong impact on corruption level, and those countries that have larger/smaller gender inequality in their parliaments are faced with higher/lower corruption, respectively. Meanwhile, there is no enough evidence that supports the relationship between gender inequality in the labor market and corruption, and the results indicate that gender inequality in the labor market is not directly linked to the corruption level.

Keywords: corruption, female labor force participation, politics, gender inequality

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Authors: Tomoaki Hashimoto

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Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the validity of the obtained stability condition.

Keywords: computational simulations, optimal control, predictive control, stochastic systems, discrete-time systems

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Authors: Xiaobao Han, Huacong Li, Jia Li

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For dynamic decoupling of linear parameter varying system, a robust dominance pre-compensator design method is given. The parameterized pre-compensator design problem is converted into optimal problem constrained with parameterized linear matrix inequalities (PLMI); To solve this problem, firstly, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameterized Lyapunov function (PLF) and pre-compensator. Then the problem was reduced to a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a newly constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator was achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation of a turbofan engine PLPV model.

Keywords: linear parameter varying (LPV), parameterized Lyapunov function (PLF), linear matrix inequalities (LMI), diagonal dominance pre-compensator

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Authors: Francesco Colcerasa, Fabio Pisani

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We contribute to the subjective well-being literature testing the relationship between life satisfaction and inequality of opportunity in health, measured through the Human Opportunity Index calculated at the national level using individual socio-economic data from the cross-country European Social Survey sample. We compute several indexes of opportunity inequality in health, each obtained according to a different combination of circumstances (gender, immigrant status, parents’ education). We find a robust and significant relationship where life satisfaction is higher in correspondence with low levels of health opportunity inequality. The result is twofold. On the one hand, the importance of the well-being of other types of inequality than income inequality emerges. On the other hand, the socioeconomic roots of inequality in health are investigated, suggesting that circumstances at birth have a role in future well-being. Several rationales for the nexus between life satisfaction and inequality of opportunity in health are possible, which we investigate by splitting the sample. Among others, we find a prominent role of pro-social preferences – formalized as interest towards own offspring (which can be interpreted as intergenerational justice) – as a mediating factor of the relationship.

Keywords: Inequality of opportunity, subjective wellbeing, health, health inequality, inequality of opportunity in health

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Authors: Albin Wallace

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Part of the provision within educational institutions is the design, commissioning and implementation of ICT facilities to improve teaching and learning. Inevitably, these facilities focus largely on Internet Protocol (IP) based provisions including access to the World Wide Web, email, interactive software and hardware tools. Educators should be committed to the use of ICT to improve learning and teaching as well as to issues relating to the Internet and educational disadvantage, especially with respect to access and exclusion concerns. In this paper I examine some recent research into the issue of inequality and use of the Internet during which I discuss the causes and consequences of exclusion in the context of social inequality, digital literacy and digital inequality, also touching on issues of global inequality.

Keywords: inequality, internet, education, design

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Authors: Quang Dong Dang

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This paper examines the possible effects of stock market developments by channels on income and wealth inequality. We use the Bayesian Multilevel Model with the explanatory variables of the market’s channels, such as accessibility, efficiency, and market health in six selected countries: the US, UK, Japan, Vietnam, Thailand, and Malaysia. We found that generally, the improvements in the stock market alleviate income inequality. However, stock market expansions in higher-income countries are likely to trigger income inequality. We also found that while enhancing the quality of channels of the stock market has counter-effects on wealth equality distributions, open accessibilities help reduce wealth inequality distributions within the scope of the study. In addition, the inverted U-shaped hypothesis seems not to be valid in six selected countries between the period from 2006 to 2020.

Keywords: Bayesian multilevel model, income inequality, inverted u-shaped hypothesis, stock market development, wealth inequality

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Authors: H. Y. Jung, Jing Wang, J. H. Park, Hao Shen

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This brief addresses the passivity problem for neural networks with time-varying delays. The aim is focus on establishing the passivity condition of the considered neural networks.

Keywords: neural networks, passivity analysis, time-varying delays, linear matrix inequality

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Authors: Harendra Singh, Rajesh Pandey

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The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems.

Keywords: non-linear fractional variational problems, Rayleigh-Ritz method, convergence analysis, error analysis

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Authors: Shoji Katagiri

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This paper is to clarify the relationship between ICT and income inequality. To do so, we develop the general equilibrium model with ICT investment, obtain the equilibrium solutions, and then simulate the model with these solutions for some OECD countries. As a result, generally, during the corresponding periods we confirm that the relationship between ICT investment and income inequality is positive. In this mode, the increment of the ratio of ICT investment to the aggregated investment in stock enhances the capital’s share of income, and finally leads to income inequality such as the increase of the share of the top decile income. Although we confirm the positive relationship between ICT investment and income inequality, the upward trend for that relationship depends on the values of parameters for the making use of the simulations and these parameters are not deterministic in the magnitudes on the calculated results for the simulations.

Keywords: ICT, inequality, capital accumulation, technology

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Authors: Morteza Faghfouri

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In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold.

Keywords: integral submanifolds, S-space forms, doubly warped product, inequality

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Authors: Shoji Katagiri

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This study deals with wage inequality in organization and shows the relationship between ICT and wage in organization. To do so, we incorporate ICT’s factors in organization into our model. ICT’s factors are efficiencies of Enterprise Resource Planning (ERP), Computer Assisted Design/Computer Assisted Manufacturing (CAD/CAM), and NETWORK. The improvement of ICT’s factors decrease the learning cost to solve problem pertaining to the hierarchy in organization. The improvement of NETWORK increases the wage inequality within workers and decreases within managers and entrepreneurs. The improvements of CAD/CAM and ERP increases the wage inequality within all agent, and partially increase it between the agents in hierarchy.

Keywords: endogenous economic growth, ICT, inequality, capital accumulation

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