Stability of highly nonlinear neutral stochastic delay system with both stable and unstable subsystems

Abstract

AbstractThe article addresses the exponentially stable conditions of the highly nonlinear neutral stochastic delayed system (HNNSDS) that contains unstable subsystems apart from stable ones under Markov switching. By the application of the mode‐dependent average dwell time (MDADT) as well as Lyapunov function approach, the general switching condition still satisfies even when the partial Lyapunov coefficients are negative. In addition, the degree of instability is combined with the study of switching signals. On this basis, the case when the system contains only stable subsystems is also investigated. A well‐known switching condition is obtained, establish the foundation of the comparison with more complex cases involving unstable subsystems. The simulation processes are eventually provided to verify rationality of the obtained criteria.