Stability Analysis of Markovian Jump System With Multi-Time-Varying Disturbances Based on Improved Interactive Convex Inequality and Positive Definite Condition

Time-varying disturbances not only exist in the external delay of Markovian jump system but also may exist in the transfer rate of internal probability transfer. This paper put forward an improved interactive convex inequality method for Markovian jump system (MJS) with multi-time-varying disturbances: time-varying delays and time-varying transition rates of probability transfer. On this basis, an improved Lyapunov function is quoted to more approximate the actual system, and the optimization of positive definite conditions of the matrix in Lyapunov functional is discussed, the specific positive definite condition is improved. At the end of this paper, the effectiveness of the above methods is verified by several simulations.