Stabilization of highly nonlinear hybrid neutral stochastic differential equations with multiple time-varying delays and different structures

Abstract

In this paper, the stabilization of a class of hybrid differently structured neutral stochastic differential equations with multiple time-varying delays is taken into consideration. The coefficients of these hybrid neutral stochastic differential delay equations with Markov switching (hybrid NSDDEs) are highly nonlinear in some modes while satisfying linear growth criteria in others. To ensure the existence and uniqueness of the solution, mild conditions are first applied to the system coefficients. Second, design techniques for discrete-time feedback control for only some of the modes are offered in order to stabilize the above systems that are unstable. New M-matrix criteria that are simple to calculate and verify are also proposed for the control functions. Then, a new theory on asymptotic and exponential stabilization is developed by using the Lyapunov function technique. Finally, the results are demonstrated with an example.