Reachable Set Estimation for Uncertain Markovian Jump Systems with Time-Varying Delay and Disturbances

In this paper, we are concerned with the problem of reachable set estimation for uncertain Markovian jump systems with time-varying delays and disturbances. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set of Markovian jump system as small as possible. Based on an augmented Lyapunov-Krasovskii functional, by dividing the time-varying delay into two nonuniform subintervals, more general delay-dependent stability criteria for the existence of a desired ellipsoid are derived. An optimized integral inequality which is based on distinguished Wirtinger integral inequality and reciprocally convex combination inequality is used to deal with the integral terms. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Automated summary

This paper focuses on the reachable set estimation for uncertain Markovian jump systems with time-varying delays and disturbances, aiming to find a proper method to minimize the no-ellipsoidal bound of the reachable set. By utilizing an augmented Lyapunov-Krasovskii functional and dividing the time-varying delay into nonuniform subintervals, more general delay-dependent stability criteria are derived. An optimized integral inequality is used to handle integral terms, and numerical examples are presented to demonstrate the effectiveness of the theoretical results.