Stabilization Analysis Of A Hybrid Stochastic Differential Equation With Polytopic Uncertainties

In recent years,with the actual application requiring the higher complexity of the system,scholars have started to pay more attention to the stability and stabilization problem of stochastic systems with polytopic uncertainty.This kind of stochastic system often appears in random failures and maintenance of element,interconnection subsystem and environment mutation models,and it really has wide research value.In this paper,the stabilization problem of hybrid stochastic system with polytopic uncertainty based on discrete observation data is studied.This thesis consists of two parts mainly.In the first part,the hybrid system with polytopic uncertainty is unstable,and add state feedback controller based on discrete observation to the drift and diffusion coefficients on the system to make the control system exponentially stable.The original hybrid system doesn't have a delay which is introduced by adding the controller later.Furthermore,the part applies the method of Lyapunov function to analyze the control system to get the stability condition and determine criterion of time delay.The second part considers the problem with the variable time delay based on the first part.That is to say,in the unstable hybrid system with variable time delay,the controller with time delay is added in the drift term and diffusion term,which makes the hybrid system exponentially stable.The time delay is a bounded function of t.Use the Razumikhin method to get the best boundary of ? which is between two consecutive state observation.This part proves the criteria of two cases : delay independent and delay dependent.The paper applies the LMI method to solve the coefficient matrix of the control term,and the same numerical example is given to verify the conclusion of part one and the first case of part two.The paper puts Markoian switching in Stochastic Differential Equations with polytopic uncertainty.This kind of system can describe some systems in real life and reflect the tiny change of system more accurately.In the design process of the controller,the general method is to use continuous observation data,but the paper designs a feedback controller based on the discrete observation data,which is more economical and effective in practical applications.