Output-feedback control design of semi-Markovian jump systems with incomplete probability description

This paper investigates the output-feedback control problem of semi-Markovian jump systems (semi-MJSs) with incomplete probability description. First, an observer-based control is designed to ensure the stochastic stability of the resultant closed-loop system and to guarantee the minimum $H_{\infty}$ performance, where the sojourn time is characterized by the mode-transition-dependent distributions. Then, a finite number of LMIs is obtained via a relaxation method that incorporates some valuable constraints on transition rates into the control design process.