Stability of stochastic functional differential equations with random switching and applications

This paper develops a new stability theory for stochastic functional differential systems with random switching. It examines general systems that are time inhomogeneous, past-dependent, and perturbed by a Brownian motion and modulated by a switching process. In contrast to the advances in the literature, this paper provides weaker and more verifiable conditions. Examples and discussion are also given to demonstrate the applicability of our results.