Delay‐dependent stability of non‐linear hybrid stochastic functional differential equations

Abstract

This study investigates delay-dependent stability of a class of highly non-linear stochastic functional differential equations with Markovian switching. Some novel boundedness and stability criteria are first established, including stability in , asymptotic stability in and almost surely asymptotic stability, based on Lyapunov functions and generalised Ito formula. Concretely, the authors generalise and improve the existing results to the hybrid stochastic functional differential equations case. An example is presented to illustrate the effectiveness of the obtained results.