Pinning control for stabilization of coupled stochastic strict-feedback nonlinear systems

This article introduces a novel class of coupled stochastic strict-feedback nonlinear systems (CSSFNSs) whose topology is not strongly connected. We are devoted to investigating the stabilization issue of CSSFNSs via pinning control. First, the specific form of controllers is decided through the back-stepping method and the design of virtual controllers. Second, we find a new method to construct the global Lyapunov function of CSSFNS by employing the Lyapunov function of each stochastic strict-feedback nonlinear system (SSFNS). Meanwhile, combining Lyapunov method with graph theory, several sufficient conditions to guarantee exponential stability in mean square of CSSFNS are obtained in the form of coefficients-type criterion. Ultimately, our theoretical results are applied to a class of coupled oscillator systems and a predator-prey model. Furthermore, the validity and feasibility of the theoretical results are illustrated by some numerical simulations.