Stability analysis of the stochastic strict-feedback nonlinear systems with time-varying delays on networks under pinning control

Abstract

This paper is concerned with the stability analysis of the stochastic strict-feedback nonlinear systems with time-varying delays on networks (SSNSTDN) via pinning control. Different from the previous literature, the new model we studied owns the non-strongly connected topology. The actual controllers are realised by back-stepping and designing virtual controllers. In particular, a novel method for constructing global Lyapunov functions is proposed,which exploits the Lyapunov function of each stochastic strict-feedback nonlinear systems with time-varying delays (SSNSTD) to construct the global Lyapunov function of SSNSTDN. Meanwhile, combining the Lyapunov method with graph theory, several sufficient conditions to guarantee the exponential stability in mean square of SSNSTDN are obtained in the form of coefficients-type criterion. Furthermore, we apply our main results to investigating the stabilisation of stochastic coupled oscillators with time-varying delays on networks and the effectiveness of proposed theories is illustrated by some numerical examples.