Homogeneous polynomial Lyapunov functions for the admissibility analysis of uncertain descriptor systems

2017 ◽  
Author(s):  
Ana Carolina dos Santos Paulino ◽  
Gabriela Iuliana Bara
Keyword(s):  
Lyapunov Functions ◽  
Homogeneous Polynomial ◽  
Descriptor Systems

Robust Analysis of LFR Systems Through Homogeneous Polynomial Lyapunov Functions

2004 ◽  
Vol 49 (7) ◽  
pp. 1211-1216 ◽  
Author(s):  
G. Chesi ◽  
A. Garulli ◽  
A. Tesi ◽  
A. Vicino
Keyword(s):  
Lyapunov Functions ◽  
Homogeneous Polynomial ◽  
Robust Analysis

Admissible Conditions for T-S Fuzzy Descriptor Systems with Non-Differentiable Membership Functions

2013 ◽  
Vol 415 ◽  
pp. 259-266
Author(s):  
Peng Lin ◽  
Gang Hu
Keyword(s):  
Continuous Time ◽  
Lyapunov Functions ◽  
Closed Loop ◽  
Structural Information ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Membership Functions ◽  
Matrix Inequalities ◽  
Closed Loop Systems ◽  
Takagi Sugeno

In this paper, the admissible conditions (regular, impulse-free and stable) for a class of continuous-time Takagi-Sugeno (T-S) fuzzy descriptor systems are investigated. Sufficient admissible conditions for the closed-loop systems under non-parallel distributed compensation (non-PDC) feedback are proposed. This approach is mainly based on the state space division properly to make the membership functions continuous differentiable. Moreover, in order to make good use of the systems’ structural information in rules, the provided conditions are obtained through fuzzy Lyapunov functions candidate and can be formulated in terms of dilated Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed approach is shown through numerical example by using the optimization toolbox.

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