SOS Stability Conditions for Nonlinear Systems Based on a Polynomial Fuzzy Lyapunov Function

2011 ◽  
Vol 44 (1) ◽  
pp. 12777-12782 ◽  
Author(s):  
Kevin Guelton ◽  
Noureddine Manamanni ◽  
Darius L. Koumba-Emianiwe ◽  
Cuong Duong Chinh
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Stability Conditions ◽  
Fuzzy Lyapunov Function

Absolute Stability of a Class of Singular Nonlinear Systems with Set-Valued Mappings

2014 ◽  
Vol 24 (01) ◽  
pp. 1550015 ◽  
Author(s):  
Gaoming Feng ◽  
Xingguo Tan
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Absolute Stability ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Delay Systems ◽  
Set Valued Mappings ◽  
The Absolute

A class of singular nonlinear systems with set-valued mappings are studied in this paper. Criteria are given based on the Lyapunov function to check the absolute stability of the systems, then the results are extended to the time delay systems and the time delay systems with uncertainty. Three examples are simulated to show the effectiveness of the proposed stability conditions.

FUZZY LYAPUNOV METHOD FOR STABILITY CONDITIONS OF NONLINEAR SYSTEMS

2006 ◽  
Vol 15 (02) ◽  
pp. 163-171 ◽  
Author(s):  
CHENG-WU CHEN ◽  
WEI-LING CHIANG ◽  
CHUNG-HUNG TSAI ◽  
CHEN-YUAN CHEN ◽  
MORRIS H. L. WANG
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Functions ◽  
Lyapunov Method ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Asymptotic Stable ◽  
Fuzzy Lyapunov Function ◽  
Quadratic Lyapunov Functions

This paper proposes a fuzzy Lyapunov method for stability analysis of nonlinear systems represented by Tagagi-Sugeno (T-S) fuzzy model. The fuzzy Lyapunov function is defined in fuzzy blending quadratic Lyapunov functions. Based on fuzzy Lyapunov functions, some stability conditions are derived to ensure nonlinear systems are asymptotic stable. By using parallel distributed compensation (PDC) scheme, we design a nonlinear fuzzy controller for the nonlinear system. This control problem will be reformulated into linear matrix inequalities (LMI) problem.

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