A delay-partitioning approach to the stability analysis of discrete-time systems

• Published in: Automatica (Oxford) Vol. 46; no. 3; pp. 610 - 614
• Main Authors: Meng, Xiangyu, Lam, James, Du, Baozhu, Gao, Huijun
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.03.2010; Elsevier
• Subjects: Applied sciences; Asymptotic stability; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Criteria; Delay; Delay systems; Discrete-time systems; Exact sciences and technology; Mathematical analysis; Mathematical models; Partitioning; Partitions; Stability; Stability analysis; Discrete-time systems; Delay systems; Asymptotic stability; Time varying system; Discrete time; Linear matrix inequality; Delay system; Stability criterion; Lyapunov function
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2009.12.004

This paper revisits the problem of stability analysis for linear discrete-time systems with time-varying delay in the state. By utilizing the delay partitioning idea, new stability criteria are proposed in terms of linear matrix inequalities (LMIs). These conditions are developed based on a novel Lyapunov functional. In addition to delay dependence, the obtained conditions are also dependent on the partitioning size. We have also established that the conservatism of the conditions is a non-increasing function of the number of partitions. Numerical examples are given to illustrate the effectiveness and advantage of the proposed methods.