New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities

This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems (MJTDSs), whose transition rates are incompletely known. In order to reduce the computational complexity and achieve better performance, auxiliary function-based double integral inequality is combined with extended Wirtinger's inequality and Jensen inequality to deal with the double integral and the triple integral in augmented Lyapunov-Krasovskii function (ALKF) and their weak infinitesimal generator respectively, the more accurate approximation bounds with a fewer variables are derived. As a result, less conservative stability criteria are proposed in this paper. Finally, numerical examples are given to show the effectiveness and the merits of the proposed method.