Stability analysis for positive Markov jump systems in [formula omitted]th moment sense: Necessary and sufficient conditions

Abstract

This paper focuses on the stability analysis and synthesis of positive Markov jump systems (PMJSs) in pth moment sense, including stability, strong stability, observability, and detectability. First, by the ℋ-representation technique, the extended system method is constructed. With the help of the extended system method, stability analysis of PMJSs in pth moment sense are transformed into those of the extended systems. Furthermore, the necessary and sufficient conditions for stability, observability, and detectability in pth moment sense are obtained. Moreover, the definitions of pth moment strong stability (PMSS) and pth moment stability threshold (PMST) are given for the first time, and the sufficient/necessary conditions for these are derived, respectively. In addition, the problems of stabilization and strong stabilization in pth moment sense are considered. Finally, several examples are presented to show the effectiveness of the obtained results.