New results on finite-time stability of singular Markovian jump systems with time-varying delay

In this paper, we focus on the finite-time stability problem of singular Markovian jump systems with time-varying delay. Firstly, this paper presents some new inequalities which are very important to the finite-time stability problem of the considered systems. Secondly, by employing these new inequalities and the Lyapunov–Krasovskii functional approach, this paper derives some sufficient conditions that guarantee the considered systems to be regular, impulse-free and finite-time stable. Finally, three numerical examples are given to illustrate the effectiveness and advantage of the proposed methods. •The finite-time stability problem for the singular Markovian systems with time-varying delay is studied in this paper.•Some new inequalities are presented in this paper.•By employing the obtained new inequalities, some new sufficient conditions which guarantee the considered systems to be regular, impulse-free and finite-time stable are derived.•Three numerical examples are given to illustrate the effectiveness and advantage of the proposed methods.