Improved stabilization conditions for Takagi-Sugeno fuzzy systems via fuzzy integral lyapunov functions

2011 ◽  
Author(s):  
Eduardo S. Tognetti ◽  
Ricardo C. L. F. Oliveira ◽  
Pedro L. D. Peres
Keyword(s):  
Lyapunov Functions ◽  
Fuzzy Systems ◽  
Fuzzy Integral ◽  
Takagi Sugeno

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.

Generalized non-monotonic Lyapunov functions for analysis and synthesis of Takagi-Sugeno fuzzy systems

2020 ◽  
Vol 39 (3) ◽  
pp. 4147-4158
Author(s):  
Pedro H.S. Coutinho ◽  
Márcia L.C. Peixoto ◽  
Márcio J. Lacerda ◽  
Miguel Bernal ◽  
Reinaldo M. Palhares
Keyword(s):  
Lyapunov Functions ◽  
Fuzzy Systems ◽  
State Of The Art ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Current State ◽  
Quadratic Lyapunov Functions ◽  
Analysis And Synthesis ◽  
Takagi Sugeno

This paper presents new stability and stabilisation conditions in the form of linear matrix inequalities for discrete-time Takagi-Sugeno fuzzy systems; they are derived considering a class of non-quadratic Lyapunov functions with multi-parametric non-monotonic terms, which significantly enhances the feasibility set of current state-of-the-art results. In addition, extensions to cope with the disturbance attenuation control problem are included. Benchmark numerical examples are provided to illustrate the effectiveness of the proposed approach.

scholarly journals Synthesis of an LMI-based fuzzy control system with guaranteed cost performance: a piecewise Lyapunov approach

2006 ◽  
Vol 17 (2) ◽  
pp. 213-225 ◽  
Author(s):  
Natache S. D. Arrifano ◽  
Vilma A. Oliveira ◽  
Lúcia V. Cossi
Keyword(s):  
Lyapunov Functions ◽  
Fuzzy Systems ◽  
State Feedback ◽  
Linear Matrix ◽  
Cost Performance ◽  
Lyapunov Approach ◽  
Analysis And Design ◽  
Quadratic Lyapunov Functions ◽  
Guaranteed Cost ◽  
Takagi Sugeno

A new stability analysis and design of a fuzzy switching control based on uncertain Takagi-Sugeno fuzzy systems are proposed. The fuzzy system adopted is composed by a family of local linear uncertain systems with aggregation. The control design proposed uses local state feedback gains obtained from an optimization problem with guaranteed cost performance formulated in the context of linear matrix inequalities and a fuzzy switching scheme built from local Lyapunov functions. The global stability is guaranteed by considering a class of piecewise quadratic Lyapunov functions. Examples are given to illustrate the applicability of the proposed approach.

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