Complementary Results on the Stability Bounds of Singularly Perturbed Systems

Cao, Liyu; Schwartz, Howard M.

doi:10.1109/tac.2004.837546

Cited by 59 publications

(33 citation statements)

References 10 publications

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“…Consider multi-parameter singularly perturbed system [22,23]. However, these results are limited to single-parameter singularly perturbed systems.…”

Section: Multi-parameter Singularly Perturbed Systemsmentioning

confidence: 99%

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Robustness analysis of descriptor systems with parameter uncertainties

Yang

Zhang

et al. 2010

Int. J. Control Autom. Syst.

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This paper investigates the problem of robustness analysis for descriptor systems with parameter uncertainties in both the derivative and state matrices. Using a parameter dependent Lyapunov function, we derive a linear matrix inequality (LMI) based sufficient condition for the admissibility of the system. Unlike the existing results, our criterion has no restriction on the rank of the derivative matrix. Further, we use the obtained method to study interval descriptor systems and multi-parameter singular perturbed systems. The proposed approaches overcome some drawbacks of the existing results. Finally, we present two numerical examples to show the effectiveness of the main results.

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“…Consider multi-parameter singularly perturbed system [22,23]. However, these results are limited to single-parameter singularly perturbed systems.…”

Section: Multi-parameter Singularly Perturbed Systemsmentioning

confidence: 99%

“…When 1 2 , ε ε = the exact stability bound of system (39) is 0.98 (see [22] and [23]). When 1 2 , ε ε ≠ the results of [22] and [23] are invalid.…”

Section: E Ementioning

confidence: 99%

Robustness analysis of descriptor systems with parameter uncertainties

Yang

Zhang

et al. 2010

Int. J. Control Autom. Syst.

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“…It is important to obtain the -bound such that stability and other performances of SPSs can be ensured. Studies on -bound can be mainly divided into two types: one only presents sufficient conditions for the existence of the -bound [10,11], and the other proposes methods to estimate the -bound [9,12]. Singularly perturbed switched systems (SPSSs) consist of a group of SPSs and a certain switching law, which specifies the active SPS at the switching instance.…”

Section: Introductionmentioning

confidence: 99%

H_∞ Control for T‐S Fuzzy Singularly Perturbed Switched Systems

Wang

Zhou

Dai

et al. 2017

Mathematical Problems in Engineering

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This paper is concerned with the design of fuzzy controller with guaranteed ∞ performance for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed switched systems. First, by using the average dwell time approach together with the piecewise Lyapunov function technique, a state feedback controller that depends on the singular perturbation parameter is developed. This controller is shown to work well for all ∈ (0, 0 ]. Then, for sufficiently small , an -independent controller design method is proposed. Furthermore, under the -independent controller, the -bound estimation problem of the overall switched closed-loop system is solved. Finally, an inverted pendulum system is used to evaluate the feasibility and effectiveness of the obtained results.

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“…As a result, it has attracted increasing interest in the past several decades. In [5], an approach to characterize and compute the stability bound is presented for continuous-time singularly perturbed systems. By considering critical stability criteria with a bialternate product, systematic approaches to determine the exact stability bound of discrete-time singularly perturbed systems are given in [13,18].…”

Section: Introductionmentioning

confidence: 99%

“…h Appendix D. Proof of Lemma 5 Proof. (22) can be rewritten as follows, W 31 ðkÞ B w ðaðkÞÞ ÀQ ðaðk þ 1ÞÞ Ã W 41 ðkÞ D zw ðaðkÞÞ where W 31 ðkÞ, W 41 ðkÞ are the same as in (23) and W 11 ðkÞ ¼ E QðaðkÞÞE À SðaðkÞ; aðk þ 1ÞÞ À S T ðaðkÞ; aðk þ 1ÞÞwhere E is same as in(5).From (42), we can obtain that W 11 ðkÞ < 0. Considering the block (3,3) of (42), then yields Q ðaðkÞÞ > 0.…”

mentioning

confidence: 99%