Stability analysis for polynomial fuzzy systems based on line-integral fuzzy Lyapunov function: A copositive relaxation approach

2017 ◽  
Author(s):  
Jairo Moreno Saenz ◽  
Motoyasu Tanaka ◽  
Kazuo Tanaka
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Fuzzy Systems ◽  
Line Integral ◽  
Polynomial Fuzzy Systems ◽  
Fuzzy Lyapunov Function ◽  
On Line

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.

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