Abstract
Problem statement: This study is concerned with the problem of delay- dependent stability analysis for discrete-time systems with interval-li ke time-varying delays. Conclusion/Recommendations: The problem is solved by applying a novel Lyapunov functional and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality. into account. It is worth noting that the closed-lo op system resulting from a delayed controller is actua lly a time-delay system. Therefore, stability results o f time-delay systems could be applied to design time- delayed controller. The present study a new Lyapunov functional, an improved delay-dependent stability criterion for discrete-time systems with time-varying delays is presented in terms of LMIs. It is shown that the obtained result is less conservative than those in. Example is providing, respectively, to demonstrate the reduced conservatism of the proposed stability crit erion and the effectiveness of the proposed design method . Preliminaries: Lemma 2.1 (Agarwal, 2000) the zero solution of difference system is asymptotic stabili ty if there exists a positive definite function n
Highlights
INTRODUCTIONThe problem of delay-dependent stability analysis for time-delay systems has received considerable attention and lots of significant results have been reported; see, for example, Chen et al
The problem of delay-dependent stability analysis for time-delay systems has received considerable attention and lots of significant results have been reported; see, for example, Chen et al.(2003), Bellomo and Bellouquid, 2006; Brezzi et al., 2007; El-Said and EL-Sherbeny, 2005; Lekhmissi, 2006) and the references therein
We note that the delay-dependent stability problem for discrete-time systems with interval-like time-varying delays (i.e., the delay d (k) satisfies
Summary
The problem of delay-dependent stability analysis for time-delay systems has received considerable attention and lots of significant results have been reported; see, for example, Chen et al. (2003), Bellomo and Bellouquid, 2006; Brezzi et al., 2007; El-Said and EL-Sherbeny, 2005; Lekhmissi, 2006) and the references therein Among these references, we note that the delay-dependent stability problem for discrete-time systems with interval-like time-varying delays (i.e., the delay d (k) satisfies. The present study a new Lyapunov functional, an improved delay-dependent stability criterion for discrete-time systems with time-varying delays is presented in terms of LMIs. It is shown that the obtained result is less conservative than those in. The discrete timedelay system (1) is asymptotically stable for any time delay h (k) satisfying 0< (k)≤h, if there exist symmetric positive definite matrices P, G, W satisfying the following matrix inequalities: ψ
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