An improved summation inequality to discrete-time systems with time-varying delay. (December 2016)

• Record Type: Journal Article
• Authors: Zhang, Chuan-Ke; He, Yong; Jiang, Lin; Wu, Min
• Is Part Of: Automatica. Volume 74(2016)
• Page Start: 10
• Page End: 15
• Publication Date: 2016-12
• Subjects: Discrete-time system -- Time-varying delay -- Summation inequality -- Linear matrix inequality; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.07.040
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: The summation inequality plays an important role in developing delay-dependent criteria for discrete-time systems with time-varying delay. This note proposes an improved summation inequality to estimate the summation terms appearing in the forward difference of Lyapunov–Krasovskii functional. Compared with the inequality recently developed by the Wirtinger-based summation inequality and the reciprocally convex lemma, the proposed one reduces the estimation gap while requires the same number of decision variables. A relaxed stability criterion of a linear discrete-time system with a time-varying delay is established by using such novel inequality. Two numerical examples are given to demonstrate the advantages of the proposed method.