Robust Suboptimal Control of Hybrid Stochastic Systems With Time-Delay

Abstract

A class of hybrid in state control system which modelled as a finite family of differential equations with time-delay is considered. Each model of this family describes the individual mode of the system. The discontinuous transitions between these modes are described by the homogeneous Markov chain. The purpose of the presented paper is to obtain a constant (nonswitching) state feedback control law, which guarantees asymptotic stability in the mean square independently on transition probabilities of the Markov chain and with arbitrary time-delay. The approach to the solution is based on the second method of Lyapunov with using the Lyapunov-Krasovskii functional. The control law is obtained through solving linear matrix equations and linear matrix inequalities.