A new delay-dependent exponential stability criterion for Itô stochastic systems with Markovian switching and time-varying delay

Abstract

On the basis of the Lyapunov–Krasovskii method, the exponential stability in the mean square sense is investigated for Itô stochastic systems with Markovian switching and time-varying delay. The statistic properties of the Markov process and Brownian motion are employed to compute the constructed Lyapunov–Krasovskii functional of a rather general form. This enables us to make sense of the challenging problems in the stochastic framework, and then find a way to extend the techniques developed in the deterministic framework. Therefore, the stability conditions are established with the aid of some slack matrices and the boundary conditions on time-varying delay. Numerical examples are given to demonstrate the reduced conservatism.

Keywords:

• stochastic systems
• time-delay
• Brownian motion
• Markov process
• stability in the mean square sense

Acknowledgement

The authors would like to thank the anonymous reviewers for their helpful and insightful comments for improving the quality and presentation of this article.