Robust stabilization for arbitrarily switched linear systems with time-varying delays and uncertainties

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.