| The discrete semi-Markov jump system is a class of a class of Multimodal ran-dom hybrid systems.This system is represented by the differential difference equa-tions,and is described by a semi-Markov chain and switches between modes with a certain probability.Due to the diversity of modes,the study of the dynamics proper-ties of the discrete semi-Markov hopping system has become a hot topic at home and abroad.This paper mainly focuses on the stability problem of discrete semi-Markov jump linear systems.The study content included the following.1.This paper studies the stability problem of discrete semi-Markov jump lin-ear system with asynchronous control and partially unknown semi-Markov kernels.By constructing Lyapunov functions related to mode correlation and residence time,and using semi-Markov kernel methods combined with linear matrix inequality(L-MI)techniques,σ-mean square stability conditions related to partially unknown semi-Markov kernels are obtained.Finally,the effectiveness and superiority of the obtained results are verified by numerical examples.2.This article studies the stability problem of discrete hidden semi-Markov jump linear systems.By constructing appropriate Lyapunov functions and combining semi-Markov kernels with emission probabilities,σ-mean square stability conditions of dis-crete hidden semi-Markov jump linear systems are obtained,which are presented in the form of linear matrix inequalities(LMI).Finally,the effectiveness of the obtained results is verified by numerical examples.3.The H_∞asynchronous control problem of discrete-time uncertain hidden Markov jump linear systems was studied.By introducing hidden Markov models and con-structing appropriate Lyapunov functions,the emission probabilities were incorporat-ed using the semi-Markov kernel method and LMI method to ensure that the studied discrete system isσ-mean square stable and satisfies H_∞performance control.Finally,the effectiveness of the method was verified through numerical examples. |
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