Discrete feedback control for highly nonlinear neutral stochastic delay differential equations with Markovian switching

Abstract

In this article, it is proved that feedback controllers can be designed to stabilize nonlinear neutral stochastic systems with Markovian switching (NSDDEwMS in short) only by using discrete observed state sequences. Due to the superlinear coefficients, the neutral term and the discrete observation data, many routine methods and techniques for the study of stochastic systems are not applicable. A new Lyapunov functional is constructed by using multiple M-matrices to prove that a given unstable NSDDEwMS can be stabilized if the control function can be designed to meet a couple of easy-to-be-verified rules. Finally, an example is given to illustrate the feasibility of the theoretical results.