Applications of a Markov Process

This chapter studies the applications of a Markov process on deterministic singular systems whose parameters are only with one mode. The first application is on an uncertain singular system which has norm bounded uncertainties on system matrices. According to the maximum singular value of uncertainty, the uncertainty set is separated into several different subsets. Then, the original system without jumping is transformed into an MJS, whose switching probability of subsets is considered in system analysis and synthesis. New version of BRL is developed by exploiting an uncertainty-dependent Lyapunov function. Two conditions for uncertainty-dependent controllers are established. Based on the key idea, the time-varying delay of the singular system is described by a Markov process, whose distribution property is also considered. Sufficient conditions for the solvability of delay-distribution-dependent stability with both exact known or uncertain TRMs are derived, and state feedback controllers depending on such a distribution are designed via the LMI approach.