scholarly journals Robust Stability for a Class of Uncertain Singularly Perturbed Systems with Multiple Time Delays.

2001 ◽  
Vol 44 (3) ◽  
pp. 900-906
Author(s):  
Ching-Fa CHEN ◽  
Shing-Tai PAN ◽  
Jer-Guang HSIEH
Keyword(s):  
Robust Stability ◽  
Time Delays ◽  
Singularly Perturbed ◽  
Multiple Time ◽  
Singularly Perturbed Systems ◽  
Multiple Time Delays ◽  
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.

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

2002 ◽  
Vol 124 (3) ◽  
pp. 467-472 ◽  
Author(s):  
Ching-Fa Chen ◽  
Shing-Tai Pan ◽  
Jer-Guang Hsieh
Keyword(s):  
Robust Stability ◽  
Stability Problem ◽  
Time Delays ◽  
Singularly Perturbed ◽  
Multiple Time ◽  
Singularly Perturbed Systems ◽  
Multiple Time Delays ◽  
Perturbed Linear Systems ◽  
Delay Dependent ◽  
Bounded Perturbations

In this paper, the robust stability problem for a class of nominally stable uncertain discrete singularly perturbed linear systems with multiple time delays is considered. A stability criterion for the slow and fast subsystems is first derived. A delay-dependent criterion is then proposed to guarantee the robust stability of the system subject to norm-bounded perturbations. A numerical example is provided to illustrate our main results.

Robust stability of uncertain linear systems with multiple time delays

1997 ◽  
Vol 211 (3) ◽  
pp. 195-202
Author(s):  
Y Fang
Keyword(s):  
Linear Systems ◽  
Robust Stability ◽  
Time Delays ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Multiple Time ◽  
Time Delay Systems ◽  
Multiple Time Delays ◽  
Uncertain Linear Systems

In this paper, the robust stability of uncertain linear systems with multiple time delays is studied. Sufficient conditions for robust stability of linear time delay systems with convex perturbations are obtained. From these sufficient conditions, a few results on robust stability of systems with other perturbations are derived. Some previously known sufficient conditions are generalized.

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