Relaxed Stabilization Criterion for T–S Fuzzy Systems by Minimum-Type Piecewise-Lyapunov-Function-Based Switching Fuzzy Controller

2012 ◽  
Vol 20 (6) ◽  
pp. 1166-1173 ◽  
Author(s):  
Ying-Jen Chen ◽  
H. Ohtake ◽  
K. Tanaka ◽  
Wen-June Wang ◽  
H. O. Wang
Keyword(s):  
Lyapunov Function ◽  
Fuzzy Systems ◽  
Fuzzy Controller ◽  
Piecewise Lyapunov Function

Global non-quadratic Lyapunov-based stabilization of T–S fuzzy systems: A descriptor approach

2020 ◽  
Vol 26 (19-20) ◽  
pp. 1765-1778
Author(s):  
Navid Vafamand
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Global Stability ◽  
Fuzzy System ◽  
Fuzzy Systems ◽  
Closed Loop ◽  
Fuzzy Controller ◽  
Performance Criteria ◽  
Membership Functions ◽  
Quadratic Lyapunov Function

This article studies the problem of global stability of the Takagi–Sugeno fuzzy systems based on a novel descriptor-based non-quadratic Lyapunov function. A modified non-quadratic Lyapunov function, which comprises an integral term of the membership functions, and a modified non-parallel distributed controller constructed by constant delayed premise variables are considered that assure the global stability of the closed-loop T–S fuzzy system. The special structure of the used non-quadratic Lyapunov function results in time-delayed terms of the membership functions, instead of appearing their time derivatives, which is the well-known issue of the common non-quadratic Lyapunov functions in the literature. Also, the memory fuzzy controller is chosen such that the artificial constant delay-dependent stability analysis conditions for a non-delayed closed-loop T–S fuzzy system are formulated in terms of linear matrix inequalities. To further reduce the conservatives, some slack matrices are introduced by deploying the descriptor representation and decoupling lemmas. Moreover, the design of the robust fuzzy controller is studied through the [Formula: see text] performance criteria. The main advantages of the proposed approach are its small conservatives and the global stability analysis, which distinguish it from the state-of-the-art methods. To show the merits of the proposed approach, comparison results are provided, and two numerical case studies, namely, flexible joint robot and two-link joint robot are considered.

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