Existence of stationary distribution for stochastic coupled nonlinear strict-feedback systems with Markovian switching

In this paper, a class of stochastic coupled nonlinear strict-feedback systems with Markovian switching (SCNSSMs) are introduced, and the existence of stationary distribution for SCNSSMs under pinning control is studied for the first time. In particular, an appropriate technique for handling the impact of Markovian switching is proposed in the process of designing virtual controllers through the back-stepping method. Regarding the global Lyapunov function for an SCNSSM, we first construct a quartic Lyapunov function for each stochastic nonlinear strict-feedback system with Markovian switching of the SCNSSM, and then combine graph theory to construct the global Lyapunov function. After that, the theoretical results are applied to stochastic coupled oscillator systems with Markovian switching. Finally, the effectiveness of proposed results is verified by some numerical simulations.