Stability analysis of hybrid stochastic delay differential equations with asynchronous switching and discrete observations

Abstract

AbstractThis paper studies the hybrid stochastic delay differential equations (SDDEs) with asynchronous switching and discrete observations. For SDDEs based on discrete observations, there are two methods: The discrete‐time approach and the input time delay method. For linear solvable equations, the discrete‐time approach is feasible but for unsolvable nonlinear hybrid SDSs, the results of the discrete‐time approach have not been discussed. So, it is natural to ask: Is the discrete‐time approach still workable for nonlinear hybrid SDSs? This paper focuses on this problem. By using tools of stochastic analysis, constructing Lyapunov functional and using the discrete‐time approach, the stability of hybrid SDSs by discrete‐time feedback control is obtained. Finally, a numerical example is presented to verify the theoretical result.