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 Based Fuzzy Control of a Wing Doubled Fractional-Order Chaos

2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Bin Wang ◽  
Yuzhu Wang ◽  
Hongbo Cao ◽  
Delan Zhu
Keyword(s):  
Fuzzy Control ◽  
Fractional Order ◽  
Stability Condition ◽  
Fuzzy Model ◽  
Original System ◽  
Circuit Diagram ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Absolute Value ◽  
Theoretical Results

This paper investigates a new wing doubled fractional-order chaos and its control. Firstly, a new fractional-order chaos is proposed, replacing linear termxin the second equation by its absolute value; a new improved system is got, which can make the wing of the original system doubled. Then, circuit diagram is presented for the proposed fractional-order chaos. Furthermore, based on fractional-order stability theory and T-S fuzzy model, a more practical stability condition for fuzzy control of the proposed fractional-order chaos is given assset of linear matrix inequality (LMI) and the strict mathematical norms of LMI are presented. Finally, numerical simulations are given to verify the effectiveness of the proposed theoretical results.

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 Reconstruction Procedure Associated with Switching Lyapunov Function for Relaxing Stability Assurance of T-S Fuzzy Mode

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Yau-Tarng Juang ◽  
Chih-Peng Huang ◽  
Chung-Lin Yan
Keyword(s):  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Fuzzy Model ◽  
Alternative Form ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
State Variables ◽  
Stability Criteria ◽  
Quadratic Lyapunov Function ◽  
Reconstruction Procedure

This paper proposes a novel reconstruction procedure to lessen the conservatism of stability assurance of T-S Fuzzy Mode. By dividing the state variables into some bounded regions, the considered T-S fuzzy model can be first transferred to an alternative form via a reconstructing procedure. Thus, we can attain some relaxing stability criteria based on the switching quadratic Lyapunov function (SQLF) method. Notably, these proposed conditions are explicitly formulated by linear matrix inequality (LMI) form and can handily be evaluated by current software tools. Finally some illustrative examples are given to experimentally demonstrate the validity and merit of the proposed method.

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.

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