Mean square stability and H2-control of continuous-time jump linear systems with partial information on the Markov parameter

This paper studies the mean square stabilizability and H2-control problems for continuous-time Markov Jump Linear Systems (MJLS) assuming that the controller has access only to a detector that provides information on the jump parameter. The goal is to design a feedback linear controller using this detector information that stochastically stabilizes the closed loop system and provides a H2 guaranteed cost. A Linear Matrix Inequalities (LMI) formulation is derived in order to achieve these goals. The formulation encompasses the cases with perfect information, no information and those considered in [1]. A numerical example illustrates the obtained results.