Stability condition of continuous Takagi-Sugeno fuzzy system based on fuzzy Lyapunov function

2011 ◽  
Author(s):  
Yassine Manai
Keyword(s):  
Lyapunov Function ◽  
Stability Condition ◽  
Fuzzy System ◽  
Fuzzy Lyapunov Function ◽  
Takagi Sugeno

Observer-based robust H∞ control for uncertain Markovian jump systems via fuzzy Lyapunov function

2018 ◽  
Vol 41 (3) ◽  
pp. 657-667 ◽  
Author(s):  
Jun Chen ◽  
Tieqing He ◽  
Fei Liu
Keyword(s):  
Lyapunov Function ◽  
External Disturbance ◽  
Optimization Techniques ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Congruent Transformation ◽  
Fuzzy Lyapunov Function ◽  
Jump Systems ◽  
Takagi Sugeno

This paper investigates the problem of observer-based robust [Formula: see text] control for a class of continuous-time nonlinear Markovian jump systems (MJSs) with uncertainties, external disturbance and unavailable states that can be represented by Takagi-Sugeno (T-S) fuzzy models. Based on a mode-dependent fuzzy Lyapunov function and by introducing slack matrix variables, a sufficient condition for the existence of the state observer and observer-based robust [Formula: see text] controller for such MJSs are derived by constructing an augmented fuzzy system. Further, by means of congruent transformation in matrix and linear matrix inequality (LMI) method, the results are given in the form of LMIs that can be easily solved by using the convex optimization techniques. Moreover, we also give the result obtained via common stochastic Lyapunov function to compare with the proposed approach. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

Stability analysis of Takagi–Sugeno systems using a switched fuzzy Lyapunov function

2021 ◽  
Vol 543 ◽  
pp. 43-57
Author(s):  
Leandro J. Elias ◽  
Flávio A. Faria ◽  
Rayza Araujo ◽  
Vilma A. Oliveira
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Fuzzy Lyapunov Function ◽  
Takagi Sugeno
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