Finite-time Boundedness Analysis And Control For Stochastic Systems With Impulsive Effects

In recent years,in most practical engineering systems,impulsive jump and stochastic noise disturbance are two important factors that need to be considered.As a class of important hybrid system,impulsive stochastic system consider two factors that impulsive jump and stochastic noise disturbance,which attract the interest of many scholars.However,most scholars tend to pay attention to the steady-state performance of the system,in communication networks,aircraft maneuvers and robot control systems,because of the short working time of these systems,people should pay more attention to these systems in addition to the steady performance of these systems,whether a certain transient performance is satisfied.Later,the concept of finite time stability is proposed to solve the transient performance of the system.However,only considering the finite time stability of the system is still not comprehensive,because most systems can not avoid the influence of external interference.At this time,the finite time bounded problem of the system should be considered.In this regard,this paper analyzes the finite time boundedness of several kinds of stochastic systems with impulsive effects in the case of external interference,and obtains some results.The specific contents are as follows:1.By using the Lyapunov function method,the average impulsive interval method and the Schur complementary lemma,the finite time boundedness of a class of time delay impulsive stochastic system is studied,and a sufficient condition for the finite time mean square bounded by the linear matrix inequality(LMIs)is obtained.On the basis of the finite time bounded conditions,the state feedback stabilization controller and the observer based dynamic output feedback controller are designed to ensure that the closed loop system is also bounded by the finite time mean square.Finally,a numerical example is given to illustrate the effectiveness of the proposed method.2.By using the Lyapunov-Krasovskii functional method,the average impulsive interval method,the Gronwall inequality and the Schur complementary lemma,the finite time boundedness of a class of time-delay impulsive stochastic system is further studied.A sufficient condition for finite time mean square boundedness is given in the form of linear matrix inequalities(LMIs).Then,based on the bounded conditions,the design scheme of a state feedback stabilization controller with time delay is given to ensure that the closed loop system is bounded by the finite time mean square.Finally,a numerical example is given to illustrate the effectiveness of the proposed method.