Observer-Based Controller Design for Discrete-Time Markovian Jump Linear Systems With Partial Information

In this paper, the observer-based controller problem is considered for a class of discrete-time Markovian jump systems with partial information. We consider the situation that the parameters on Markov chain discussed in this paper may not be totally observed, which is different from the traditional case with complete information on Markov parameters. First, although the operating modes are not completely available, one kind of detector submitting the information on operating modes is provided. Then, a kind of observer and an observer-based controller are constructed in order to achieve the observation of system state and assure the stabilization of the closed-loop systems, respectively. At the same time, sufficient conditions on the existence of the observer and the corresponding controller are presented in terms of linear matrix inequalities (LMIs). Finally, the simulations illustrate the advantage and potential application of the proposed theoretical results.