Title: Improved robust stability and stabilisation conditions for discrete-time linear systems with time-varying delay

Authors: M. Venkatesh; Sourav Patra; Goshaidas Ray

Addresses: Department of Electrical Engineering, Indian Institute of Technology Kharagpur, West Bengal, 721302, India ' Department of Electrical Engineering, Indian Institute of Technology Kharagpur, West Bengal, 721302, India ' Heritage Institute of Technology, Chowbaga Road, Kolkata, West Bengal, India

Abstract: This paper presents robust stability and stabilisation problems of linear discrete-time systems with interval time-varying state-delay. By invoking a new Lyapunov-Krasovskii functional, a less conservative delay-dependent robust stability criterion is derived in terms of linear matrix inequalities (LMIs) using the summation inequality in combination with the extended reciprocally convex inequality. Then, a delay-dependent stabilisation problem of discrete-time systems is explored by designing a state feedback controller. The superiority of the proposed result over existing ones is demonstrated through numerical examples.

Keywords: time-delay systems; robust stability; stabilisation; summation inequality; Lyapunov-Krasovskii functional; extended reciprocally convex inequality; linear matrix inequality.

DOI: 10.1504/IJAAC.2022.125284

International Journal of Automation and Control, 2022 Vol.16 No.5, pp.547 - 572

Received: 01 Oct 2019
Accepted: 21 Nov 2019
Published online: 06 Sep 2022 *

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