Stabilisation in distribution of hybrid stochastic differential equations by feedback control based on discrete-time state observations

A new concept of stabilisation of hybrid stochastic systems in distribution by feedback controls based on discrete-time state observations is initialised. This is to design a controller to stabilise the unstable system such that the distribution of the solution process tends to a probability distribution. In addition, the discrete-time state observations are also taken into consideration to make the design of the controller more practical. Theorems on the stabilisation of hybrid stochastic systems in distribution are proved. The lower bound of the duration between two consecutive state observations is obtained. The implementation of theorems are demonstrated by designing the feedback controls in the structure cases and easy-to-rules are provided for the user. Numerical examples are discussed to illustrate the theoretical results.