Research On Discrete Stabilization Of Nonlinear Hybrid Stochastic System

Hybrid stochastic systems are a class of typical dynamic systems.The stabilization of unstable nonlinear hybrid stochastic system is a hot topic in recent years.For the problem of the stabilization of unstable highly nonlinear hybrid stochastic system,the unstable highly nonlinear hybrid stochastic system can become stable by using the feedback controller based on discrete observations of state and mode.The specific content includes the following several aspects:Firstly,the research background,significance and status of discrete feedback control and hybrid stochastic system are introduced which lays a theoretical foundation for the qualitative research of hybrid stochastic systems.Secondly,It(?) formula,common inequalities,lemmas and related theories of stochastic differential equations are introduced in order to study the existence and uniqueness theorem of hybrid stochastic system with Markov switching and the expression of explicit solution are given.Then,the stabilization theory of continuous random noise and discrete random noise to unstable nonlinear differential system are introduced.The continuous random noise can make the unstable nonlinear differential system stable exponentially,and the delayed random noise based on discrete observation of state and mode can make the unstable nonlinear differential system stable almost surely exponentially.Finally,we study the stabilization of unstable high nonlinear hybrid stochastic systems with feedback controllers based on discrete state and mode observations.Under the local Lipschitz condition and polynomial growth condition,the hybrid stochastic differential system may be unstable.On the basis of previous ideas,we introduce state and mode discrete feedback controller to ensure the existence and uniqueness of global solution and the global solution moment’s boundedness.Then the controlled system tends to be stable exponentially even almost surely exponentially by using the common inequalities and Borel-Cantelli’s lemma and constructing Lyapunov function.Finally,through the motion trajectories’ numerical simulation of the original system and the controlled system,the rationality of the proposed assumptions and related conclusions are verified by introducing examples.Figure 5;Table 0;Reference 54...