Stability Analysis And Control Of It? Stochastic Systems

Stability is the primary problem in the research of control systems.For some practical systems,such as aviation system and missile interception system,it is necessary to have good transient performance,that is,to constrain the state trajectory of the system.Therefore,the finite-time stability and quantitative stability have attracted wide attention.On the other hand,systems are inevitably disturbed by external factors during operation,which can be described by Ito stochastic differential equation.Ito stochastic systems have important applications in practical engineering.In this paper,the stability and control of Ito stochastic systems are studied.The main contents are as follows:(1)The finite-time H? control problem of Ito-type stochastic nonlinear systems with time-delay is studied.The state feedback and dynamic output feedback finite-time H? controllers are designed respectively.The obtained inequality conditions that meet the design requirements can not only guarantee that the closed-loop system is mean square finite-time bounded,but also determine the optimal H? control performance index.Finally,the corresponding H? control performance index is obtained by parameter optimization algorithm.(2)For a class of stochastic systems with Wiener noise and Poisson jumps,based on the proposed differential Gronwall inequality approach,the finite-time annular domain stability and stabilization are analyzed.For this kind of Ito-type stochastic linear systems,the finite-time annular domain stabilization problem is discussed from the aspects of state feedback and output feedback.Two kinds of controllers satisfying the design requirements are obtained.Finally,the influence of Poisson jump intensity on the stability of systems is obtained through the corresponding algorithm.(3)The quantitative mean square exponential stability and stabilization of linear stochastic Markov jump systems with Wiener noise and Poisson jumps are studied.By means of matrix transformation and inequality technique,the state feedback controller and observer-based controller are obtained,which can make the closed-loop system satisfy the quantitative mean square exponential stability.The results are verified by the algorithm and an example.