Robust linear filtering for discrete-time hybrid Markov linear systems

In this paper we consider the robust linear filtering of hybrid discrete-time Markovian jump linear systems. We assume that only an output of the system is available, and therefore the values of the jump parameter are not known. It is desired to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the square error. We consider uncertainties on the parameters of the possible modes of operation of the system. A linear matrix inequalities (LMI) formulation is proposed to solve the problem. For the case in which there are no uncertainties on the modes of operation of the system, we show that the LMI formulation provides a filter with the same stationary mean square error as the one obtained from the Riccati equation approach.