Finite Time Stability of Impulsive Stochastic Time-delay System with Markov Switching

For a class of impulsive stochastic systems with Markov switch and time-varying delay, the correlation criterion of mean-square finite-time stability of the system was established by using Lyapunov–Krasovskii (L–K) functional method and average impulsive interval condition. The derivative of L–K functional about time was obtained by generalized Ito ’s formula, and the derivative of L–K functional was scaled according to integral inequality to reduce the conservatism of the criterion. Combining with the condition of average impulsive interval to constrain the number of impulses in a uniform time interval, a delay-dependent stability criterion in the form of linear matrix inequality (LMI) was obtained to further reduce the conservatism of the criterion. A state feedback controller was designed to make the system meet the finite time stability, and an example was given to verify it. The results show that the correlation criterion established in this paper can further reduce the conservatism of the criterion by selecting the functional of modal correlation and using the condition of average impulsive interval.