An LMI condition for the robustness of constant-delay linear predictor feedback with respect to uncertain time-varying input delays. (November 2019)

• Record Type: Journal Article
• Authors: Lhachemi, Hugo; Prieur, Christophe; Shorten, Robert
• Is Part Of: Automatica. Volume 109(2019)
• Publication Date: 2019-11
• Subjects: Time-varying delay control -- Predictor feedback -- Robust stability -- PDEs -- Boundary control; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.108551
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper discusses the robustness of the constant-delay predictor feedback in the case of an uncertain time-varying input delay. Specifically, we study the stability of the closed-loop system when the predictor feedback is designed based on the knowledge of the nominal value of the time-varying delay. By resorting to an adequate Lyapunov–Krasovskii functional, we derive an LMI-based sufficient condition ensuring the exponential stability of the closed-loop system for small enough variations of the time-varying delay around its nominal value. These results are extended to the feedback stabilization of a class of diagonal infinite-dimensional boundary control systems in the presence of a time-varying delay in the boundary control input.