scholarly journals Stability analysis of Takagi-Sugeno fuzzy systems via LMI: methodologies based on a new fuzzy Lyapunov function

2011 ◽  
Vol 22 (6) ◽  
pp. 664-676 ◽  
Author(s):  
Leonardo Amaral Mozelli ◽  
Reinaldo Martinez Palhares
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Fuzzy Systems ◽  
Time Derivative ◽  
Time Varying ◽  
Membership Functions ◽  
Fuzzy Lyapunov Function ◽  
Numerical Tools ◽  
Takagi Sugeno ◽  
First Time

Stability analysis of TS fuzzy systems can be much improved by resorting to fuzzy Lyapunov functions, since they are parameterized by membership functions and can better characterize the time-varying feature of these systems by means of the information regarding the first time-derivative of the membership functions. In this paper an enhanced fuzzy Lyapunov function is used to develop stability conditions that evaluate also the second time-derivative of membership functions, improving the time-varying characterization of TS systems. By using diferent strategies to consider the information regarding such derivatives and employing some numerical tools that decouple system from Lyapunov function matrices new LMI tests are developed. Numerical examples illustrate the effectiveness of those methodologies.

scholarly journals A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy Models

2007 ◽  
Vol 17 (1) ◽  
pp. 39-51 ◽  
Author(s):  
Ibtissem Abdelmalek ◽  
Noureddine Goléa ◽  
Mohamed Hadjili
Keyword(s):  
Lyapunov Functions ◽  
Fuzzy Systems ◽  
Time Derivative ◽  
Stability Conditions ◽  
Membership Functions ◽  
Lyapunov Approach ◽  
Fuzzy Models ◽  
Quadratic Stabilization ◽  
Quadratic Lyapunov Functions ◽  
Takagi Sugeno

A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy ModelsIn this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.

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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