Razumikhin technique for stabilisation of highly nonlinear hybrid systems by bounded discrete-time state feedback control working intermittently

This paper applies the Razumikhin idea to study the stabilisation of hybrid stochastic systems by discrete-time state feedback control, which works intermittently and is designed boundedly. Theoretically, the Razumikhin method is generalised in view of time-varying functions, rather than constants, where the time-inhomogeneous property of intermittent control could be fully made use of. In practice, the control cost could be reduced significantly since the controller is bounded, not observed continuously and having rest time. Moreover, there will be a wider range of applications especially for models that do not satisfy the linear growth condition (say highly nonlinear). An example of the coupled Van der Pol–Duffing oscillator system is hence provided to show the practicability of the developed theory.