An improved characterization of bounded realness for singular delay systems and its applications

Abstract

SUMMARYThis paper is concerned with establishing a delay-dependent bounded real lemma (BRL) for singular systems with a time delay. Without resorting to any bounding techniques for some cross terms and model transformation, a new version of BRL for such systems is proposed, which guarantees a singular system to be regular, impulse free and stable while satisfying a prescribed H 1 performance level for any delays smaller than a given upper bound. Based on this, an H 1 state feedback controller is designed via a linear matrix inequality approach. The BRL, stability as well as H 1 results developed in this paper are less conservative than existing ones in the literature, which is demonstrated by providing some numerical examples.

H∞ filtering for singular systems with time‐varying delay

“…In addition, the stability conditions and BRLs proposed by [27][28][29][30][31] are invalid for this example.…”

Finite-time stability and stabilization of singular state-delay systems using improved estimation of a lower bound on a Lyapunov-like functional

“…Using Theorem 1-2 and Corollary 1-3, we are in a position to design a state feedback controller (9) such that the resultant closed-loop system (10) is regular, impulse free and finite-time stable. For practical reasons, only the problem of the stabilization based on Theorem 1 has been addressed below.…”

“…For the sake of infinite dimension of the singular time-delay systems, their dynamic behaviour is more difficult to analyse in comparison to singular non-delay systems. For this reason, over the past decades, there has been increasing interest for the stability analysis of singular time-delay systems and many results have been reported [8][9][10][11][12][13].…”

H∞ deconvolution filter design for uncertain descriptor hybrid delay systems with limited communication capacity and unknown transition rates

“…Until now, some significant topics on descriptor systems like stability and stabilization, controller problem, Correspondence to: Guangming Zhuang, E-mail: zgmtsg@ 126.com filtering problem, etc, have been widely studied and lots of meaningful results have been reported, for instance, [13][14][15][16][17][18], and the references therein. Recently, descriptor hybrid system, also known as singular Markovian jump systems (SMJSs) have attracted much attention due to the fact that the structures or parameters of singular systems sometimes changes abruptly, much important literature have been published to introduce the related results such as [11,12,[19][20][21][22][23][24][25][26][27][28][29], and so on.…”

“…Due to a given singular system must be not only stable but also regular and impulse free or causal at the same time, the investigation for singular time delay systems, especially singular time-varying delay systems, is much more complicated than that for state-space systems [14,16,[18][19][20][21]24].…”