Improved stability and stabilisation criteria for discrete time‐delay systems via a novel double summation inequality. Issue 3 (1st February 2018)

• Record Type: Journal Article
• Authors: Zhao, Tao; Liang, Weibo; Dian, Songyi; Xiao, Jian; Wei, Zhenbo
• Is Part Of: IET control theory & applications. Volume 12:Issue 3(2018)
• Page Start: 327
• Page End: 337
• Publication Date: 2018-02-01
• Subjects: stability -- stability criteria -- discrete time systems -- delays -- Lyapunov methods -- linear matrix inequalities; stabilisation criteria -- discrete time‐delay systems -- double summation inequality -- stability analysis -- augmented Lyapunov‐Krasovskii functional -- conservative stability -- stabilisation conditions -- general double summation terms -- augmented LKF forward difference -- zero equalities -- advanced convexificator techniques -- linear matrix inequalities; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2017.0791
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : This study focuses on the problem of stability analysis and stabilisation for discrete time‐delay systems. A new type of augmented Lyapunov–Krasovskii functional (LKF) is proposed to derive less conservative stability and stabilisation conditions. A novel inequality is developed to handle more general double summation terms which arise from the forward difference of augmented LKF. Several zero equalities are introduced to further relax the existing results. Using some advanced convexificator techniques, the derived stability and stabilisation conditions are presented in terms of linear matrix inequalities. Several numerical examples are provided to demonstrate the advantage of the proposed approach.