Simultaneous stabilization of a collection of uncertain discrete-time systems with time-varying state-delay via discrete-time sliding mode control. (August 2019)

• Record Type: Journal Article
• Authors: Dastaviz, A; Binazadeh, T
• Is Part Of: Journal of vibration and control. Volume 25:Number 16(2019)
• Page Start: 2261
• Page End: 2273
• Publication Date: 2019-08
• Subjects: Discrete-time systems -- time delay -- simultaneous stabilization -- sliding mode control -- linear matrix inequality; Vibration -- Periodicals; Damping (Mechanics) -- Periodicals; 620.3
• DOI: 10.1177/1077546319852485
• Languages: English
• ISSNs: 1077-5463

Abstract

This paper considers the simultaneous stabilization problem which concerns finding a single controller to simultaneously stabilize a finite collection of discrete-time nonlinear systems with time-varying state delay and norm-bounded uncertainties. For this purpose, a simultaneously stabilizing discrete-time sliding mode controller (DT-SMC) is synthesized. Based on the delay-dependent Lyapunov–Krasovskii functional method, sufficient conditions are derived which guarantee the existence of a common sliding surface in terms of a nonconvex feasibility problem. The cone complementarity linearization approach is exploited to transform the nonconvex conditions into a convex optimization problem. Finally, the robust simultaneously stabilizing DT-SMC is designed in order to draw the closed-loop trajectories of each system onto the common sliding surface in finite time and to maintain it thereafter. The effectiveness of the proposed method is investigated by simulation of a practical example.