Disturbed Chaotic Systems Synchronization via Robust Mixed Functional Projective Method

2014 ◽  
Vol 496-500 ◽  
pp. 1293-1297
Author(s):  
Tao Fan ◽  
Ning Fang ◽  
Fei Tan
Keyword(s):  
State Feedback ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Generalized Synchronization ◽  
Linear State ◽  
Control And Synchronization

Robust mixed functional projective synchronization (RMFPS), which is the generalized synchronization idea developed very recently, is investigated in this paper. Based on Lyapunov stability theory and linear matrix inequality (LMI), some novel stability criterions for the synchronization between drive and response chaotic systems with disturbances are derived, and then a simple linear state feedback synchronization controller is designed. In order to test the proposed method, numerical simulations of hyper-chaotic unified systems with disturbances are then provided to show the effectiveness and feasibility of this chaos control and synchronization schemes.

scholarly journals LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1128
Author(s):  
Hamede Karami ◽  
Saleh Mobayen ◽  
Marzieh Lashkari ◽  
Farhad Bayat ◽  
Arthur Chang
Keyword(s):  
Linear Matrix Inequality ◽  
State Feedback ◽  
Chaotic Systems ◽  
Nonlinear Function ◽  
Observer Design ◽  
System Stability ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Estimation Errors ◽  
Suggested Approach

In this study, the observer-based state feedback stabilizer design for a class of chaotic systems in the existence of external perturbations and Lipchitz nonlinearities is presented. This manuscript aims to design a state feedback controller based on a state observer by the linear matrix inequality method. The conditions of linear matrix inequality guarantee the asymptotical stability of the system based on the Lyapunov theorem. The stabilizer and observer parameters are obtained using linear matrix inequalities, which make the state errors converge to the origin. The effects of the nonlinear Lipschitz perturbation and external disturbances on the system stability are then reduced. Moreover, the stabilizer and observer design techniques are investigated for the nonlinear systems with an output nonlinear function. The main advantages of the suggested approach are the convergence of estimation errors to zero, the Lyapunov stability of the closed-loop system and the elimination of the effects of perturbation and nonlinearities. Furthermore, numerical examples are used to illustrate the accuracy and reliability of the proposed approaches.

A New Criterion for Chaos Synchronization Using Linear State Feedback Control

2003 ◽  
Vol 13 (08) ◽  
pp. 2343-2351 ◽  
Author(s):  
Guo-Ping Jiang ◽  
Guanrong Chen ◽  
Wallace Kit-Sang Tang
Keyword(s):  
Feedback Control ◽  
Chaos Synchronization ◽  
State Feedback ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
State Feedback Control ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Linear State ◽  
New Criterion

This paper studies chaos synchronization between two coupled chaotic systems using linear state feedback control. A new, simple and yet easily applicable criterion is derived for chaos synchronization based on the Lyapunov stability theory and the Linear Quadratic Optimal Control theory. This criterion is given in terms of some simple algebraic inequalities established by the Gerschgorin theorem, and it is easily applicable to a large class of chaotic systems. As an example, the familiar Chua's circuit is simulated for demonstration.

Robust H2/H∞Control Strategy for Linear Markovian Jump Systems

2014 ◽  
Vol 525 ◽  
pp. 646-652
Author(s):  
Min Bian ◽  
Qing Yun Guo
Keyword(s):  
Control Strategy ◽  
State Feedback ◽  
Control Strategies ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Bounded Real Lemma ◽  
Finite State ◽  
Linear State ◽  
Feasible Solutions ◽  
Jump Systems

The robust H2/<em>H</em>∞ control strategy for a class of linear continuous-time uncertain systems with randomly jumping parameters is investigated. The transition of the jumping parameters is decided by a finite-state Markov process. The uncertainties are supposed to be norm-bounded. It is desired to design a linear state feedback control strategies such that the closed-loop system satisfies H performance and minimizes the H2 norm of the system. A sufficient condition is first established on the existence of the robust H2/<em>H</em>∞controller bases on the bounded real lemma. Then the corresponding state-feedback law is given in terms of a set of linear matrix inequalities (LMIs). It is showed that this condition is equivalent to the feasible solutions problem of LMI. Furthermore, the control strategy design problem is converted into a convex optimization problem subject to LMI constraints, which can be easily solved by standard numerical software.

scholarly journals Universal Projective Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Baojie Zhang ◽  
Hongxing Li
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Function ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Reference Systems ◽  
Unknown Parameters ◽  
Hyperchaotic Systems ◽  
Function Matrix

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme.

scholarly journals A NONLINEAR STATE FEEDBACK APPROACH TO THE CONTROL AND SYNCHRONIZATION OF CONTINUOUS-TIME CHAOTIC SYSTEMS

1999 ◽  
Vol 48 (9) ◽  
pp. 1618
Author(s):  
GAO JIN-FENG ◽  
LUO XIAN-JUE ◽  
MA XI-KUI ◽  
PAN XIU-QIN ◽  
WANG JUN-KUN
Keyword(s):  
Continuous Time ◽  
State Feedback ◽  
Chaotic Systems ◽  
Control And Synchronization ◽  
Nonlinear State

Comments on “Takagi–Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality”

2019 ◽  
Vol 26 (9-10) ◽  
pp. 643-645
Author(s):  
Xuefeng Zhang
Keyword(s):  
Fuzzy Control ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Wide Class ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Takagi Sugeno

This article shows that sufficient conditions of Theorems 1–3 and the conclusions of Lemmas 1–2 for Takasi–Sugeno fuzzy model–based fractional order systems in the study “Takagi–Sugeno fuzzy control for a wide class of fractional order chaotic systems with uncertain parameters via linear matrix inequality” do not hold as asserted by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.

scholarly journals A Novel Iterative Linear Matrix Inequality Design Procedure for Passive Inter-Substructure Vibration Control

2020 ◽  
Vol 10 (17) ◽  
pp. 5859
Author(s):  
Josep Rubió-Massegú ◽  
Francisco Palacios-Quiñonero ◽  
Josep M. Rossell ◽  
Hamid Reza Karimi
Keyword(s):  
Linear Matrix Inequality ◽  
Vibration Control ◽  
State Feedback ◽  
Optimization Problems ◽  
Seismic Protection ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Static State ◽  
Fluid Viscous Dampers ◽  
Iterative Linear Matrix Inequality

In vibration control of compound structures, inter-substructure damper (ISSD) systems exploit the out-of-phase response of different substructures to dissipate the kinetic vibrational energy by means of inter-substructure damping links. For seismic protection of multistory buildings, distributed sets of interstory fluid viscous dampers (FVDs) are ISSD systems of particular interest. The connections between distributed FVD systems and decentralized static output-feedback control allow using advanced controller-design methodologies to obtain passive ISSD systems with high-performance characteristics. A major issue of that approach is the computational difficulties associated to the numerical solution of optimization problems with structured bilinear matrix inequality constraints. In this work, we present a novel iterative linear matrix inequality procedure that can be applied to obtain enhanced suboptimal solutions for that kind of optimization problems. To demonstrate the effectiveness of the proposed methodology, we design a system of supplementary interstory FVDs for the seismic protection of a five-story building by synthesizing a decentralized static velocity-feedback H∞ controller. In the performance assessment, we compare the frequency-domain and time-domain responses of the designed FVD system with the behavior of the optimal static state-feedback H∞ controller. The obtained results indicate that the proposed approach allows designing passive ISSD systems that are capable to match the level of performance attained by optimal state-feedback active controllers.

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