Stationary Riccati equation for linear minimum mean square error estimator of Markovian jump systems

In this paper we obtain sufficient conditions for the convergence of the error covariance matrix to a stationary value for the linear minimum mean square error estimator (LMMSE) of discrete time linear systems subject to abrupt changes in the parameters modeled by a Markov chain θ(k)ε{1,...,N} (Markovian jump linear systems, MJLS). Under the assumption of mean square stability of the MJLS and ergodicity of the associated Markov chain it is shown that there exists a unique solution for the stationary Riccati filter equation, and moreover this solution is the limit of the error covariance matrix of the LMMSE. This result is suitable for designing a time-invariant stable suboptimal filter of LMMSE for MJLS