Robust guaranteed cost control for continuous-time uncertain Markov switching singular systems with mode-dependent time delays

Abstract

The guaranteed cost control problem for mode-dependent time-delay Markov switching singular systems with norm-bounded uncertain parameters is discussed. Based on delay-dependent linear matrix inequalities, sufficient conditions which ensure the nominal Markov switching singular system to be regular, non-impulsive and stochastically stable are derived by quoting a mode-dependent Lyapunov functional and applying Moon’s inequality for cross terms. The sufficient conditions involve two cases. Case 1: the time delays are known; Case 2: the time delays are unknown, but the difference of the largest and the smallest time delay is known. Then, the problem is solved to design a state-feedback control law such that the closed-loop system is stochastically stable and the corresponding cost function value is not bigger than a specified upper bound for all the admissible uncertainties. Finally, optimization algorithms are given to find the optimal performance indexes.