Stochastic stability analysis of semi-Markovian jump linear systems via a relaxation technique for time-varying transition rates

This paper investigates the stochastic stability analysis problem for a class of continuous-time semi-Markovian jump linear systems (S-MJLSs). To this end, the stability condition for S-MJLSs is first formulated in the form of two set constraints and a matrix inequality dependent on the time-varying transition rates stemming from sojourn time. And then, the sojourn-time-dependent stability condition is converted into a finite set of linear matrix inequalities (LMIs) via the use of a relaxation technique capable of considering all possible constraints associated with time-varying transition rates.