Abstract
This paper presents the asynchronous control problem of Markov jump linear systems (MJLSs) with incomplete transition descriptions. Different from most of the existing results, controller modes are asynchronous with system modes described by conditional probability matrices (CPMs) in this paper. Moreover, the information of transition rate matrices (TRMs) in continuous-time domain and transition probability matrices (TPMs) in discrete-time domain are considered to be incomplete. In continuous-time case, the necessary and sufficient conditions of stability and sufficient conditions of stabilization are derived. In discrete-time case, the necessary and sufficient conditions of stability and stabilization are derived. Finally, several numerical examples are given to illustrate the results.
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