Stabilisation of hybrid system with different structures by feedback control based on discrete-time state observations

This paper considers a class of hybrid stochastic differential equations (SDEs) with different structures in different modes. In some modes, the coefficients of the SDEs satisfy the linear growth condition, while in the other modes, the coefficients are highly nonlinear. These systems are often unstable. This paper aims to design a discrete-time feedback control which is only put in a part of modes where the coefficients are highly nonlinear, such that these systems become stable. The stabilities concerned include H _∞-stability and exponential stability in the moment, as well as almost sure stability. Finally, an example is given to illustrate these results.