Stabilization of non-homogeneous hidden semi-Markov Jump systems with limited sojourn-time information

Abstract

This paper is concerned with stability analysis and controller design for a family of non-homogeneous hidden semi-Markov jump systems (NHS-MJSs) with limited information of sojourn-time probability density functions (ST-PDFs). Motivated by the fact that accessing all real system modes is difficult in practice, hidden semi-Markov chains that are more general than semi-Markov chains are introduced to determine the mode switching of the studied system with hidden modes. By allowing for the transition probabilities of the associated embedded Markov chains depending on the operation time, the controlled system is an NHS-MJS that generalizes homogeneous hidden semi-Markov jump systems as well. The circumstance of limited knowledge of ST-PDFs is considered, which relaxes the universal assumption in hidden semi-Markov jump systems that all of PDFs must be completely known a priori. By means of a novel Lyapunov function, the conditions on the existence of a desired available-mode and elapsed-time-dependent controller are proposed, ensuring that the closed-loop NHS-MJS is mean-square stable. Three numerical examples are provided to demonstrate the superiorities of the theoretical results.