Finite-time Annular Domain Stability And Stabilization For Several Classes Of Stochastic Systems

Stochastic system is a kind of system that describes the actual operation affected by random factors such as external environmental interference,internal structure change and human intervention,such as economic system,traffic control system and intelligent manufacturing system,which has important practical application value.On the other hand,finite time annular domain stability is used to study the upper and lower bounds of state,and fully considers the transient performance requirements of the systems,such as aircraft system and financial system,which has attracted the attention of many scholars.Therefore,the finite time annular domain stability and stabilization of stochastic systems have important practical significance.The main contents are as follows:(1)For time-varying stochastic systems with Wiener and Poisson noises,the problems of finite time annular domain stability and stabilization are studied.Firstly,using It(?)-Levy formula and time-varying Lyapunov function method,a more general finite time annular domain stability condition is given,and time-varying state feedback controller and static output feedback controller with less conservatism are designed;Secondly,a new numerical algorithm for solving differential matrix inequality is presented,and the relationship between the upper and lower bounds of state trajectory and Poisson strength is given.The influence of Poisson strength on system state,transient performance and controller design is studied;Finally,a numerical example and a practical financial system model are used to verify the effectiveness of the method.(2)The finite time annular domain stability and stabilization of stochastic systems with semi-Markov mode switching are studied.Firstly,a new inequality,reverse differential Gronwall inequality,is designed to reduce the conservatism of the sufficient condition,and its advantages over the existing methods are analyzed;Secondly,the timevarying semi-Markov transition rate is made to belong to an unfixed polytope,which expands the range of transition rate;Then,a finite time annular domain stability condition,multimodal state feedback controller and observer based controller are designed;Next,a (?)×N mode algorithm is given to study the relationship between adjustable parameters and transition rate range;Finally,a numerical example is given to verify the effectiveness of the method.(3)For semi-Markov switched time-varying stochastic systems with Wiener and Poisson noises,the problems of finite time annular domain stability and stabilization are studied.Firstly,using time-varying multimode Lyapunov function and semi-Markov time-varying transition rate belonging to unfixed polytope,more general stability conditions are given,in addition,time-varying multimode state feedback controller and static output feedback controller are designed;Then,a new time-varying parameter algorithm is designed,and the relationship between Poisson strength and transition rate parameters is studied;Finally,a numerical example is used to verify the effectiveness of the proposed method.