Stability Analysis and Stabilization of Semi-Markov Jump Linear Systems with Improved Efficiency of Probabilistic Information Utilization

This article establishes a systematic methodology to improve the utilization efficiency of probabilistic information for the stability analysis and stabilizing control of discrete-time semi-Markov jump linear systems (SMJLSs). The transition and sojourn information is incompletely known, and the coupling between the known (or unknown) transition and unknown (or known) sojourn information renders the known probabilistic information difficult to be fully leveraged, which can lead to conservative results in system analysis and synthesis. To approximate the unknown transition and sojourn information, a polyhedral approach is developed, which facilitates the incorporation of the known probabilistic information coupled with unknown information. Accordingly, novel vertex-based Lyapunov functions are proposed to establish stability conditions. New criteria are established for the stability analysis and control of SMJLSs by incorporating all the jointly known transition and sojourn information, all the known probabilistic information, and both the known and the approximation of unknown probabilistic information, respectively. The effectiveness and superiority of the theoretical results are illustrated by a numerical example and a simulated continuous stirred tank reactor process.