Stability in terms of two measures of solutions to stochastic partial differential delay equations with switching

TL;DR

This paper investigates the stability of solutions to stochastic partial differential delay equations with switching, providing new sufficient conditions for stability in terms of two measures, including under specific switching conditions.

Contribution

It introduces new stability criteria for stochastic PDE delay equations with switching, extending existing results to broader switching scenarios and stability measures.

Findings

Established stability conditions based on approximating strong solutions.

Extended stability analysis to switching systems with average dwell-time.

Provided criteria under fixed-index sequence monotonicity.

Abstract

In this paper, the problem of stability in terms of two measures is considered for a class of stochastic partial differential delay equations with switching. Sufficient conditions for stability in terms of two measures are obtained based on the technique of constructing a proper approximating strong solution system and carrying out a limiting type of argument to pass on stability of strong solutions to mild ones obtained by Bao, Truman and Yuan [ J. Bao, A. Truman,C. Yuan, Stability in distribution of mild solutions to stochastic partial differential delay equations with jumps, Proc. R. Soc. A, 465, 2111-2134 (2009)]. In particular, the stochastic stability under the fixed-index sequence monotonicity condition and under the average dwell-time switching are considered.