Performance analysis for multi‐delay systems in finite frequency domains

Abstract

SUMMARY This paper considers the problem of performance analysis for continuous‐time multi‐delay systems in finite frequency domains. Unlike the existing results about the performance analysis for time‐delay systems in the entire frequency range, this study is focused on examining the performances of time‐delay systems in finite frequency ranges. Based on a further generalization of the strict S‐procedure, a delay‐dependent sufficient condition for systems to satisfy performances in finite frequency intervals is developed in the framework of linear matrix inequality approach. Finally, the effectiveness of the proposed method is illustrated via some numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.

Fault detection for singular multiple time-delay systems with application to electrical circuit

“…Corollary 1 (Zhang and Yang [34]). The finite frequency performance (S.1) with E ¼ I is satisfied for the system (37), if there exist symmetric positive definite matrices fP d3i g N i ¼ 1 , Q d and symmetric matrices P d , X di such that…”

“…□ Remark 2. In view of the Corollary 1, the result presented in [34] can be regarded as a special case of Theorem 1.…”

“…Lemma 2 (Zhang and Yang [34] Further generalization of the strict S-procedure). Let admissible set M A H P and N A H P be given and define G 1 by…”

“…Based on a frequency-domain approach, the finite frequency H 1 performance analysis problem has been investigated in [34] for system (37).…”

“…By combining time domain and frequency domain approaches, a new delay-dependent finite frequency BRL is obtained within the framework of the Parseval theorem [33] and the strict S-procedure [34]. It is shown that this BRL includes some existing results as special cases.…”