Robust Fault Estimation for a Class of T-S Fuzzy Singularly Perturbed Systems with State Time Delays

2021 ◽  
Author(s):  
Chao Sun ◽  
Qiuyuan Zeng ◽  
Shengjuan Huang ◽  
Suhuan Yi
Keyword(s):  
Time Delays ◽  
Singularly Perturbed ◽  
Fault Estimation ◽  
Singularly Perturbed Systems ◽  
State Time ◽  
Perturbed Systems

Stability Analysis for a Class of Singularly Perturbed Systems With Multiple Time Delays

2004 ◽  
Vol 126 (3) ◽  
pp. 462-466 ◽  
Author(s):  
Shing-Tai Pan ◽  
Ching-Fa Chen ◽  
Jer-Guang Hsieh
Keyword(s):  
Asymptotic Stability ◽  
Time Delays ◽  
Original System ◽  
Singularly Perturbed ◽  
Multiple Time ◽  
Singularly Perturbed Systems ◽  
Fast Subsystem ◽  
Multiple Time Delays ◽  
Perturbed Systems ◽  
Slow Subsystem

The paper is to investigate the asymptotic stability for a general class of linear time-invariant singularly perturbed systems with multiple non-commensurate time delays. It is a common practice to investigate the asymptotic stability of the original system by establishing that of its slow subsystem and fast subsystem. A frequency-domain approach is first presented to determine a sufficient condition for the asymptotic stability of the slow subsystem (reduced-order model), which is a singular system with multiple time delays, and the fast subsystem. Two delay-dependent criteria, ε-dependent and ε-independent, are then proposed in terms of the H∞-norm for the asymptotic stability of the original system. Furthermore, a simple estimate of an upper bound ε* of singular perturbation parameter ε is proposed so that the original system is asymptotically stable for any ε∈0,ε*. Two numerical examples are provided to illustrate the use of our main results.

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