Stabilization of highly nonlinear stochastic neutral Markovian jump systems with multiple delays

Abstract

This paper is concerned with the stabilization of highly nonlinear stochastic neutral Markovian jump systems (HNSNMJSs) with multiple delays. First, mild conditions are imposed on the coefficients of the system to ensure the existence and uniqueness of the solution. Second, the design method of the delayed feedback control is provided to stabilize an unstable HNSNMJS with multiple delays in the neutral term. In particular, novel conditions in terms of M-matrices are proposed for the control function, which facilitate derivation and calculation and are easy to verify. Then, by applying Lyapunov functional-based approach, new theories on the asymptotic stabilization and exponential stabilization are established. Finally, the validity of the theoretical results is illustrated through a numerical example.