Advances in Discrete-State-Feedback Stabilization of Highly Nonlinear Hybrid Systems by Razumikhin Technique

In this article, the authors apply the Razumikhin technique to investigate the stabilization of hybrid stochastic systems by feedback control based on discrete-time state observations, rather than the widely used comparison idea or Lyapunov functional method to this problem. Further, we extend the Razumikhin method to study the asymptotic boundedness of hybrid stochastic systems. The coefficients of these stochastic systems considered do not meet the usual linear growth condition, but are highly nonlinear. The control function designed can easily be implemented in reality. Meanwhile, a better bound for a class of stochastic systems could be obtained on the duration between two consecutive state observations comparing with the existing results. Two interesting examples, the application to stochastic volatility model and stochastic Cohen–Grossberg neural network, respectively, are provided to manifest the effectiveness of our new theory.