Improved Razumikhin and Krasovskii Stability Criteria for Time-Varying Stochastic Time-Delay Systems

TL;DR

This paper develops improved stability criteria for time-varying stochastic systems with delays, allowing indefinite derivatives and enhancing existing methods for analyzing p-th moment stability and input-to-state stability.

Contribution

It introduces novel Razumikhin and Krasovskii stability criteria that permit indefinite derivatives, advancing the analysis of stochastic time-delay systems with Markovian switching.

Findings

New stability criteria for stochastic systems with delays

Criteria accommodate indefinite derivatives of Lyapunov functions

Examples demonstrate effectiveness of the proposed methods

Abstract

The problem of p-th moment stability for time-varying stochastic time-delay systems with Markovian switching is investigated in this paper. Some novel stability criteria are obtained by applying the generalized Razumikhin and Krasovskii stability theorems. Both p-th moment asymptotic stability and (integral) input-to-state stability are considered based on the notion and properties of uniformly stable functions and the improved comparison principles. The established results show that time-derivatives of the constructed Razumikhin functions and Krasovskii functionals are allowed to be indefinite, which improve the existing results on this topic. By applying the obtained results for stochastic systems, we also analyze briefly the stability of time-varying deterministic time-delay systems. Finally, examples are provided to illustrate the effectiveness of the proposed results.