Zhang, Lixian, Shi, Peng ORCID: 0000-0001-8218-586X and Basin, Michael V ORCID: 0000-0002-7274-4303 (2008) Robust stabilization for arbitrarily switched linear systems with time-varying delays and uncertainties. In: Proceedings of the 47th IEEE Conference on Decision and Control. IEEE, New York, N.Y., pp. 5336-5341.

Abstract

This paper studies the robust stability and stabilization problems for switched linear discrete-time systems. The parameter uncertainties in the system under consideration are time-varying but norm-bounded, and the time delay is assumed to be time-varying and bounded, which covers the constant and mode-dependent constant delays as special cases. First, sufficient conditions are derived to guarantee the stability of the uncertain system. Then, a control law is designed so that the resulting closed-loop system is stable for all admissible uncertainties. A linear matrix inequality (LMIs) approach, together with a cone complementary linearization algorithm, is proposed to solve the above problems. A numerical example is given to show the potential applicability of the obtained theoretic results.

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