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SUMMARYThis paper is concerned with establishing a delay‐dependent bounded real lemma (BRL) for singular linear parameter‐varying (LPV) systems with time‐variant delay. In terms of linear matrix inequality, a delay‐dependent BRL is presented to ensure singular time‐delay LPV systems to be admissible and satisfy a prescribed H∞ performance level. The BRL is obtained based on the construction of a parameter‐dependent Lyapunov–Krasovskii functional. The effectiveness of the proposed approach is shown by several numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.

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Semi-Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a class of semi-Markovian systems with mode-dependent time-variant delays is investigated. By Lyapunov function approach, together with a piecewise analysis method, a sufficient condition is proposed to guarantee the stochastic stability of the underlying systems. As more time-delay information is used, our results are much less conservative than some existing ones in literature. Finally, two examples are given to show the effectiveness and advantages of the proposed techniques.On the other hand, the presence of time delay is quite common in practical dynamical systems, which is frequently the main cause of instability and poor performance of systems [14][15][16][17][18][19][20][21]. Therefore, many researchers have been attracted on Markovian jump system with time delay, and many results have been reported. To mention a few, the stability and stabilization problems are considered in [22][23][24][25]; the control problem was studied in [26][27][28][29]; H 1 filtering was addressed in [30][31][32]. In addition, much attention has been focused on the analysis and synthesis for time-delay systems with less conservativeness. In [33] and [34], the delay-partitioning method was proposed to deal with the stability and stabilization problems for time-delay MJS. The criteria are less conservative with the delay-partitioning method because this treatment makes us employ more information on time delay. As an extension of the delay-partitioning method, a piecewise analysis method (PAM) was considered in the stability analysis of the time-delay systems [35]. The idea of PAM has initially appeared in [35], and then by this approach, some stability criteria for linear time-varying delay systems with less conservativeness were presented.Motivated by the aforementioned discussion, the objective of this paper is to investigate the problem of stochastic stability for S-MJS with mode-dependent time-varying delays. Specifically, the concepts of S-MJS, and mode-dependent time-delays are introduced together for the stochastically stable problem in order to reflect a more realistic environment. By Lyapunov function approach, together with PAM, conditions are proposed to ensure the stochastic stability of the underlying S-MJS with time delays. Finally, numerical examples are given to illustrate the effectiveness of the proposed control scheme.The rest of this paper is organized as follows. The problem of stochastic stability for S-MJS with mode-dependent time-delays is formulated in Section 2. In Section 3, our main results are presented by linear matrix inequality approach. Two numerical examples are provided in Section 4 to demonstrate the effectiveness and advantages of our results, and conclusion is drawn in Section 5.Notations. The notations used ...