Search results for: Lyapunov theory

Authors: S. Henine, A. Youkana

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This work is devoted to study the global existence and asymptotic behavior of solutions for Gierer-Meinhardt systems arising in biological phenomena. We prove that the solutions are global and uniformly bounded by a positive constant independent of the time. Our technique is based on Lyapunov functional argument. Under suitable conditions, we established a result on the asymptotic behavior of solutions. These results are valid for any positive continuous initial data, and improve some recently results established.

Keywords: asymptotic behavior, Gierer-Meinhardt systems, global existence, Lyapunov functional

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Authors: Elragig Aiman, Dreiwi Hanan, Townley Stuart, Elmabrook Idriss

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In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

Keywords: diffusion driven instability, common Lyapunov function (CLF), turing pattern, positive-definite matrix

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Authors: Tet H. Yeap

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An analog restricted Hopfield Network is presented in this paper. It consists of two layers of nodes, visible and hidden nodes, connected by directional weighted paths forming a bipartite graph with no intralayer connection. An energy or Lyapunov function was derived to show that the proposed network will converge to stable states. By introducing hidden nodes, the proposed network can be trained to store patterns and has increased memory capacity. Training to be an associative memory, simulation results show that the associative memory performs better than a classical Hopfield network by being able to perform better memory recall when the input is noisy.

Keywords: restricted Hopfield network, Lyapunov function, simultaneous perturbation stochastic approximation

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Authors: Ashish Ashish

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In the last few decades, the discrete chaos of difference equations has gained a massive attention of academicians and scholars due to its tremendous applications in each and every branch of science, such as cryptography, traffic control models, secure communications, weather forecasting, and engineering. In this article, a generalized logistic discrete map is established and discrete chaos is reported through period doubling bifurcation, period three orbit and Lyapunov exponent. It is interesting to see that the generalized logistic map exhibits superior chaos due to the presence of an extra degree of freedom of an ordered parameter. The period doubling bifurcation and Lyapunov exponent are demonstrated for some particular values of parameter and the discrete chaos is determined in the sense of Devaney's definition of chaos theoretically as well as numerically. Moreover, the study discusses an extended chaos based image encryption and decryption scheme in cryptography using this novel system. Surprisingly, a larger key space for coding and more sensitive dependence on initial conditions are examined for encryption and decryption of text messages, images and videos which secure the system strongly from external cyber attacks, coding attacks, statistic attacks and differential attacks.

Keywords: chaos, period-doubling, logistic map, Lyapunov exponent, image encryption

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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: A. Ghodbane, M. Saad, J. F. Boland, C. Thibeault

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Historically, actuators’ redundancy was used to deal with faults occurring suddenly in flight systems. This technique was generally expensive, time consuming and involves increased weight and space in the system. Therefore, nowadays, the on-line fault diagnosis of actuators and accommodation plays a major role in the design of avionic systems. These approaches, known as Fault Tolerant Flight Control systems (FTFCs) are able to adapt to such sudden faults while keeping avionics systems lighter and less expensive. In this paper, a (FTFC) system based on the Geometric Approach and a Reconfigurable Flight Control (RFC) are presented. The Geometric approach is used for cosmic ray fault reconstruction, while Sliding Mode Control (SMC) based on Lyapunov stability theory is designed for the reconfiguration of the controller in order to compensate the fault effect. Matlab®/Simulink® simulations are performed to illustrate the effectiveness and robustness of the proposed flight control system against actuators’ faulty signal caused by cosmic rays. The results demonstrate the successful real-time implementation of the proposed FTFC system on a non-linear 6 DOF aircraft model.

Keywords: actuators’ faults, fault detection and diagnosis, fault tolerant flight control, sliding mode control, geometric approach for fault reconstruction, Lyapunov stability

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Authors: Iftikhar Ahmad, A. Benallegue, A. El Hadri

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In this paper, we have proposed an observer for the reconstruction and a control law for the rejection application of unknown bounded external disturbance in a dynamical system. The strategy of both the observer and the controller is designed like a second order sliding mode with a proportional-integral (PI) term. Lyapunov theory is used to prove the exponential convergence and stability. Simulations results are given to show the performance of this method.

Keywords: non-linear systems, sliding mode observer, disturbance rejection, nonlinear control

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Authors: Igor Vladimirovich Kuzminov

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The proposed article is an alternative version of the Theory of Relativity. The version is based on the concepts of classical Newtonian physics and does not deny the existing calculation base. The proposed theory completely denies Einstein's existing Theory of Relativity. The only thing that connects these theories is that the proposed theory is also built on postulates. The proposed theory is intended to establish the foundation of classical Newtonian physics. The proposed theory is intended to establish continuity in the development of the fundamentals of physics and is intended to eliminate all kinds of speculation in explanations of physical phenomena. An example of such speculation is Einstein's Theory of Relativity (E).

Keywords: the theory of relativity, postulates of the theory of relativity, criticism of Einstein's theory, classical physics

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Authors: Shabnam Pashaei, Mohammadali Badamchizadeh

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This paper presents a new fractional-order terminal sliding mode control for synchronization of two different fractional-order chaotic systems with uncertainty and external disturbances. A fractional-order integral type nonlinear switching surface is presented. Then, using the Lyapunov stability theory and sliding mode theory, a fractional-order control law is designed to synchronize two different fractional-order chaotic systems. Finally, a simulation example is presented to illustrate the performance and applicability of the proposed method. Based on numerical results, the proposed controller ensures that the states of the controlled fractional-order chaotic response system are asymptotically synchronized with the states of the drive system.

Keywords: terminal sliding mode control, fractional-order calculus, chaotic systems, synchronization

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Authors: Daniel Nkrumah

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The Magic Bullet theory was a popular media effect theory that defined the power of the mass media in altering beliefs and perceptions of its audiences. However, following the People's Choice study, the theory was said to have been disproved and was supplanted by the Two-Step Flow Theory. This paper examines the relevance of the Magic Bullet theory in Africa and establishes whether it is still relevant in Africa's media spaces and societies. Using selected cases on the continent, it adopts a grounded theory approach and explores a new theoretical model that attempts to enforce an argument that the Two-Step Flow theory though important and valid, was ill-conceived as a direct replacement to the Magic Bullet theory.

Keywords: magic bullet theory, two-step flow theory, media effects, african media

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Authors: P. W. Tsai, W. L. Hong, C. W. Chen, C. Y. Chen

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In this paper, we present a neural network (NN) based approach represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov stability, parallel particle swarm optimization, linear differential inclusion, artificial intelligence

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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 Moosavi Mohseni, Wenjun Zhang, Jiling Cao

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The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations especially rational expectation hypothesis can increase complexity of the system and leads to more chaotic behavior.

Keywords: taylor rule, monetary system, chaos theory, lyapunov exponent, GMM estimator

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Authors: Ramazan Kadiev, Arkadi Ponossov

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Semidiscrete systems contain both continuous and discrete components. This means that the dynamics is mostly continuous, but at certain instants, it is exposed to abrupt influences. Such systems naturally appear in applications, for example, in biological and ecological models as well as in the control theory. Therefore, the study of semidiscrete systems has recently attracted the attention of many specialists. Stochastic effects are an important part of any realistic approach to modeling. For example, stochasticity arises in the population dynamics, demographic and ecological due to a change in time of factors external to the system affecting the survival of the population. In control theory, random coefficients can simulate inaccuracies in measurements. It will be shown in the presentation how to incorporate such effects into semidiscrete systems. Stability analysis is an essential part of modeling real-world problems. In the presentation, it will be explained how sufficient conditions for the moment stability of solutions in terms of the coefficients for linear semidiscrete stochastic equations can be derived using non-Lyapunov technique.

Keywords: abrupt changes, exponential stability, regularization, stochastic noises

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Authors: Toshinori Nawata

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In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of nonlinear systems with constrained input is presented. When designing the control, a constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics

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Authors: Arne Fagerstrom, Gary Cunningham, Fredrik Hartwig

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In this paper, a theory of sustainable enterprises, sustainable enterprise theory (SET), is developed. The sustainable enterprise theory can only be a valid theory if knowledge about life and nature is complete. Knowledge limitations should not stop enterprises from doing business with a goal of better long-term life on earth. Life demands stewardship of the resources used during one’s lifetime. This paper develops a model influenced by (the classical) enterprise theory and resource theory that includes more than money in the business activities of an enterprise. The sustainable enterprise theory is then used in an analysis of accountability and in discussions about sustainable businesses.

Keywords: sustainable business, sustainability reporting, sustainable values, theory of the firm

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Authors: Kreangkri Ratchagit

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This paper is concerned with exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, timevarying delays, Lyapunov-Krasovskii functional, Leibniz-Newton’s formula

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Authors: Mamyrbek A. Beisenbi, Nurgul M. Kissikova, Saltanat E. Beisembina, Salamat T. Suleimenova, Samal A. Kaliyeva

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The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.

Keywords: gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability

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Authors: Grienggrai Rajchakit

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This paper is concerned with the exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton's formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, time-varying delays, lyapunov-krasovskii functional, leibniz-newton's formula

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Authors: Jalal Eddine Benmansour, Khouane Boulanoir, Nacera Bekhadda, Elhassen Benfriha

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This paper introduces a novel composite control approach that addresses the challenge of stabilizing the three-axis attitude of a flexible satellite in the presence of vibrations caused by flexible appendages. The key contribution of this research lies in the development of a disturbance observer, which effectively observes and estimates the unwanted torques induced by the vibrations. By utilizing the estimated disturbance, the proposed approach enables efficient compensation for the detrimental effects of vibrations on the satellite system. To govern the attitude angles of the spacecraft, a proportional derivative controller (PD) is specifically designed and proposed. The PD controller ensures precise control over all attitude angles, facilitating stable and accurate spacecraft maneuvering. In order to demonstrate the global stability of the system, the Lyapunov method, a well-established technique in control theory, is employed. Through rigorous analysis, the Lyapunov method verifies the convergence of system dynamics, providing strong evidence of system stability. To evaluate the performance and efficacy of the proposed control algorithm, extensive simulations are conducted. The simulation results validate the effectiveness of the combined approach, showcasing significant improvements in the stabilization and control of the satellite's attitude, even in the presence of disruptive vibrations from flexible appendages. This novel composite control approach presented in this paper contributes to the advancement of satellite attitude control techniques, offering a promising solution for achieving enhanced stability and precision in challenging operational environments.

Keywords: attitude control, flexible satellite, vibration control, disturbance observer

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Authors: Feleke Tsegaye

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The work in this thesis mainly focuses on trajectory tracking of fixed wing unmanned aerial vehicle (FWUAV) by using fuzzy based sliding mode controller(FSMC) for surveillance applications. Unmanned Aerial Vehicles (UAVs) are general-purpose aircraft built to fly autonomously. This technology is applied in a variety of sectors, including the military, to improve defense, surveillance, and logistics. The model of FWUAV is complex due to its high non-linearity and coupling effect. In this thesis, input decoupling is done through extracting the dominant inputs during the design of the controller and considering the remaining inputs as uncertainty. The proper and steady flight maneuvering of UAVs under uncertain and unstable circumstances is the most critical problem for researchers studying UAVs. A FSMC technique was suggested to tackle the complexity of FWUAV systems. The trajectory tracking control algorithm primarily uses the sliding-mode (SM) variable structure control method to address the system’s control issue. In the SM control, a fuzzy logic control(FLC) algorithm is utilized in place of the discontinuous phase of the SM controller to reduce the chattering impact. In the reaching and sliding stages of SM control, Lyapunov theory is used to assure finite-time convergence. A comparison between the conventional SM controller and the suggested controller is done in relation to the chattering effect as well as tracking performance. It is evident that the chattering is effectively reduced, the suggested controller provides a quick response with a minimum steady-state error, and the controller is robust in the face of unknown disturbances. The designed control strategy is simulated with the nonlinear model of FWUAV using the MATLAB® / Simulink® environments. The simulation result shows the suggested controller operates effectively, maintains an aircraft’s stability, and will hold the aircraft’s targeted flight path despite the presence of uncertainty and disturbances.

Keywords: fixed-wing UAVs, sliding mode controller, fuzzy logic controller, chattering, coupling effect, surveillance, finite-time convergence, Lyapunov theory, flight path

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Authors: Pauline E. Ngo-Henha

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Existing turnover intention theories are reviewed in this paper. This review was conducted with the help of the search keyword “turnover intention theories” in Google Scholar during the month of July 2017. These theories include: The Theory of Organizational Equilibrium (TOE), Social Exchange Theory, Job Embeddedness Theory, Herzberg’s Two-Factor Theory, the Resource-Based View, Equity Theory, Human Capital Theory, and the Expectancy Theory. One of the limitations of this review paper is that data were only collected from Google Scholar where many papers were sometimes not freely accessible. However, this paper attempts to contribute to the research in clarifying the distinction between theories and models in the context of turnover intention.

Keywords: Literature Review, Theory, Turnover, Turnover intention

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Authors: Manlika Ratchagit

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This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: robust mean square stability, discrete-time stochastic systems, hybrid systems, interval time-varying delays, Lyapunov functional, linear matrix inequalities

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Authors: Manlika Rajchakit

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This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: robust mean square stability, discrete-time stochastic systems, hybrid systems, interval time-varying delays, lyapunov functional, linear matrix inequalities

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Authors: Nisha Budhwar, Sunita Daniel

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In this paper, we analyse the stability of the SEIR model of malaria with infective immigrants which was recently formulated by the authors. The model consists of an SEIR model for the human population and SI Model for the mosquitoes. Susceptible humans become infected after they are bitten by infectious mosquitoes and move on to the Exposed, Infected and Recovered classes respectively. The susceptible mosquito becomes infected after biting an infected person and remains infected till death. We calculate the reproduction number R0 using the next generation method and then discuss about the stability of the equilibrium points. We use the Lyapunov function to show the global stability of the equilibrium points.

Keywords: equilibrium points, exposed, global stability, infective immigrants, Lyapunov function, recovered, reproduction number, susceptible

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Authors: Richard L. Summers

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The advanced computational analysis of biological systems is becoming increasingly dependent upon an understanding of the information-theoretic structure of the materials, energy and interactive processes that comprise those systems. The stability and survival of these living systems are fundamentally contingent upon their ability to acquire and process the meaning of information concerning the physical state of its biological continuum (biocontinuum). The drive for adaptive system reconciliation of a divergence from steady-state within this biocontinuum can be described by an information metric-based formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of Kullback-Leibler information minimization driven by survival replicator dynamics. If the mathematical expression of this process is the Lagrangian integrand for any change within the biocontinuum then it can also be considered as an action functional for the living system. In the direct method of Lyapunov, such a summarizing mathematical formulation of global system behavior based on the driving forces of energy currents and constraints within the system can serve as a platform for the analysis of stability. As the system evolves in time in response to biocontinuum perturbations, the summarizing function then conveys information about its overall stability. This stability information portends survival and therefore has absolute existential meaning for the living system. The first derivative of the Lyapunov energy information function will have a negative trajectory toward a system's steady state if the driving force is dissipating. By contrast, system instability leading to system dissolution will have a positive trajectory. The direction and magnitude of the vector for the trajectory then serves as a quantifiable signature of the meaning associated with the living system’s stability information, homeostasis and survival potential.

Keywords: meaning, information, Lyapunov, living systems

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

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This paper studies a secondary voltage control framework of the microgrids based on the consensus for a communication network of multiagent. The proposed control is designed by the communication network with one-way links. The communication network is modeled by a directed graph. At this time, the concept of sampling is considered as the communication constraint among each distributed generator in the microgrids. To analyze the sampling effects on the secondary voltage control of the microgrids, by using Lyapunov theory and some mathematical techniques, the sufficient condition for such problem will be established regarding linear matrix inequality (LMI). Finally, some simulation results are given to illustrate the necessity of the consideration of the sampling effects on the secondary voltage control of the microgrids.

Keywords: microgrids, secondary control, multiagent, sampling, LMI

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Authors: Mohammad Sahadet Hossain, Shamsil Arifeen, Mehrab Hossian Likhon

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In this paper, we analyze a linear time invariant (LTI) descriptor system of large dimension. Since these systems are difficult to simulate, compute and store, we attempt to reduce this large system using Low Rank Cholesky Factorized Alternating Directions Implicit (LRCF-ADI) iteration followed by Square Root Balanced Truncation. LRCF-ADI solves the dual Lyapunov equations of the large system and gives low-rank Cholesky factors of the gramians as the solution. Using these cholesky factors, we compute the Hankel singular values via singular value decomposition. Later, implementing square root balanced truncation, the reduced system is obtained. The bode plots of original and lower order systems are used to show that the magnitude and phase responses are same for both the systems.

Keywords: low-rank cholesky factor alternating directions implicit iteration, LTI Descriptor system, Lyapunov equations, Square-root balanced truncation

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Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen

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In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm

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Authors: Mohammad Ahmadi

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Argumentative writing is a highly opinion-based form of discourse that necessitates the ability to address commonly held opinions (endoxa). To enhance the development of persuasive, argumentative essays, the incorporation of classical rhetorical theory, with a specific focus on topics related to the canon of Invention (inventio), can be advantageous. This research investigates the practical application of rhetorical theory in teaching students how to construct compelling argumentative essays. The fundamental premise of this study is the limited familiarity of rhetoric and composition students with rhetorical theory. Consequently, this paper presents an effective pedagogical approach to introduce rhetorical theory to students, beginning from a foundational level. It delineates the procedures and progression that educators should adopt to elucidate and facilitate students' comprehension of rhetorical theory while demonstrating its utilization in the writing of an argumentative essay.

Keywords: argumentative essay, rhetorical theory, pedagogy, invention

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