Asynchronous stabilization for hidden Markov jump linear systems with complex transition probabilities

Abstract

This study is intended to investigate the asynchronous stabilization problem for discrete-time Markov jump linear systems (MJLSs) with complex mode transition probabilities (C-TPs). A practical scenario is considered in this study. First, the system mode may not always be precisely detected in practice, therefore a hidden Markov model (HMM) is used to characterize the mismatched mode phenomenon. Second, some mode TPs associated with the Markov process of the original system may be unknown or inaccurate, rendering the C-TPs scenario. This issue could also exist in the conditional TPs associated with the joint process of the HMM. A mode separation strategy is proposed to separate the Markov process and the joint process such that we can deal with the C-TPs associated with them, respectively. Based on the above considerations, a unified controller design framework is established for MJLSs with or without C-TPs. Moreover, the results developed in this study can cover some existing works as special cases without introducing additional conservativeness. A DC motor device is used to demonstrate the effectiveness of the proposed design method.