Stability and dissipativity analysis for uncertain Markovian jump systems with random delays via new approach

This paper studies the problem of stability and dissipativity analysis for uncertain Markovian jump systems (UMJSs) with random time-varying delays. Based on the auxiliary function-based integral inequality (AFBII) and with the help of some mathematical tools, a new double integral inequality (NDII) is developed. Then, to show the efficiency of the proposed inequality, a suitable Lyapunov-Krasovskii functional (LKF) is constructed with augmented delay-dependent terms. By employing integral inequalities, new delay-dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are given to show the effectiveness and less conservatism of the results.