Linear matrix inequality criteria for robust synchronization of uncertain fractional-order chaotic systems

2011 ◽  
Vol 21 (4) ◽  
pp. 043107 ◽  
Author(s):  
Liping Chen ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Robust Synchronization

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.

GLOBAL ROBUST SYNCHRONIZATION OF A CLASS OF NONAUTONOMOUS CHAOTIC SYSTEMS WITH PARAMETER MISMATCH VIA VARIABLE SUBSTITUTION CONTROL

2011 ◽  
Vol 21 (05) ◽  
pp. 1369-1382 ◽  
Author(s):  
YUN CHEN ◽  
XIAOFENG WU ◽  
ZHIFANG GUI
Keyword(s):  
Linear Matrix Inequality ◽  
Chaotic Systems ◽  
Phase Mismatch ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Single Variable ◽  
Parameter Mismatch ◽  
Robust Synchronization ◽  
Variable Substitution

This paper investigates global robust synchronization of a class of nonautonomous chaotic systems with parameter mismatch under the master–slave variable substitution control. A criterion of linear matrix inequality (LMI) for the global robust synchronization is rigorously proven and the corresponding synchronization error bound is analytically estimated. The LMI criterion is then applied to the gyrostat systems, obtaining some simple and optimized algebraic criteria for global robust synchronization of the master–slave gyrostat systems with time-varying phase mismatch under single-variable substitution configurations, further verified in a numerical example.

Linear Matrix Inequality Based Fractional Integral Sliding-Mode Control of Uncertain Fractional-Order Nonlinear Systems

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Sara Dadras ◽  
Soodeh Dadras ◽  
HamidReza Momeni
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Sliding Mode ◽  
Superior Performance ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Matrix Inequality ◽  
Sliding Surface ◽  
Switching Law

A design of linear matrix inequality (LMI)-based fractional-order surface for sliding-mode controller of a class of uncertain fractional-order nonlinear systems (FO-NSs) is proposed in this paper. A new switching law is achieved guaranteeing the reachability condition. This control law is established to obtain a sliding-mode controller (SMC) capable of deriving the state trajectories onto the fractional-order integral switching surface and maintain the sliding motion. Using LMIs, a sufficient condition for existence of the sliding surface is derived which ensures the t−α asymptotical stability on the sliding surface. Through a numerical example, the superior performance of the new fractional-order sliding mode controller is illustrated in comparison with a previously proposed method.

scholarly journals Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Bin Wang ◽  
Hongbo Cao ◽  
Yuzhu Wang ◽  
Delan Zhu
Keyword(s):  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Stability Condition ◽  
Chaos Synchronization ◽  
Linear Time ◽  
Three Dimensional ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Integer Order

This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI) interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D) chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.

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.

Global Sliding Mode Control Via Linear Matrix Inequality Approach for Uncertain Chaotic Systems With Input Nonlinearities and Multiple Delays

2018 ◽  
Vol 13 (3) ◽  
Author(s):  
Mona Afshari ◽  
Saleh Mobayen ◽  
Rahman Hajmohammadi ◽  
Dumitru Baleanu
Keyword(s):  
Sliding Mode Control ◽  
Linear Matrix Inequality ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Matrix Inequality ◽  
Mode Control ◽  
Global Sliding Mode Control ◽  
Uncertain Chaotic Systems

This paper considers a global sliding mode control (GSMC) approach for the stabilization of uncertain chaotic systems with multiple delays and input nonlinearities. By designing the global sliding mode surface, the offered scheme eliminates reaching phase problem. The offered control law is formulated based on state estimation, Lyapunov–Krasovskii stability theory, and linear matrix inequality (LMI) technique which present the asymptotic stability conditions. Moreover, the proposed design approach guarantees the robustness against multiple delays, nonlinear inputs, nonlinear functions, external disturbances, and parametric uncertainties. Simulation results for the presented controller demonstrate the efficiency and feasibility of the suggested procedure.

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