Asynchronous Control of Positive Markov Jump Systems: A Necessary and Sufficient Condition

This paper deals with h -gain controller synthesis of positive Markov jump systems (PMJSs) with asynchronous modes. Thanks to the hidden Markov model, the closed-loop systems are modeled as hidden Markov jump systems (HMJSs). The definitions of positivity, mean stability, and h -gain are introduced for HMJSs. A necessary and sufficient condition is derived to ensure that the HMJSs are positive and mean stable with h -gain γ that can be solvable by linear programming strategy. Two numerical examples are listed to show the effectiveness of our results.