Stability of Stochastic Functional Differential Equations with Past-Dependent Random Switching Involving Countably Infinite States

This work is devoted to stochastic functional differential equations with past-dependent random switching, in which the switching process is allowed to take values in a countable state space. Such processes are rather versatile and arise in a wide variety of applications. A central issue considered in this paper is stability. The conditions provided are more general than the existing work. After getting the desired stability results, several applications, including linear systems, linearization of nonlinear systems, multiagent systems consentability, and networked control systems are examined. Numerical results are also provided to demonstrate our results.