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

• Autores: Hugo Lhachemi, Christophe Prieur, Robert Shorten
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Nº. 109, 2019
• Idioma: inglés
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• Resumen

  • 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.