Finite-time Annular Domain Bounded Control Of Stochastic Systems

The control problems of stochastic systems have attracted much attention in physics,biology,engineering and other practical systems in the last decades.However,most of the existing research results on stochastic systems are based on the stability of Lyapunov.The Lyapunov asymptotically stable systems may have very poor transient characteristics,which is not allowed in practical engineering systems.In order to solve the transient performance problems of the systems,the concept of finite-time stability is proposed.Since the systems are often affected by external disturblunce during operation,considering the impact of external disturblunce on the state change of the system,the concept of finite-time bounded has been introduced.Finite-time stability and bounded only consider the upper bound of the system orbit,not its lower bound.Concern about the lower bound of the system orbit also has great significance in some practical problems.Considering the lower bound of the system orbit,the finite-time annular domain bounded control problems of stochastic systems are presented,and the concept of finite-time annular domain bounded control is obtained.In this paper,linear/nonlinear stochastic systems are discussed,the specific content is as follows:(1)The problem of finite-time annular domain bounded control for linear timedelay stochastic systems with(x,u,v)related noise is studied.Firstly,the definition of the finite-time annular domain bounded of the system and some lemmas are given.Secondly,two finite-time annular domain bounded controllers,one state feedback controller and the other dynamic output feedback controller,are designed to ensure finitetime annular domain bounded of the closed-loop system.In addition,an algorithm is provided to deal with the obtained matrix inequalities.Finally,two examples are given to prove the validity of the results.(2)The problem of finite-time annular domain bounded control of It?-type stochastic systems with wiener and poisson random disturbance is studied.Firstly,the definition of the finite-time annular domain bounded of the system and some lemmas are given.Secondly,two finite-time annular domain bounded controllers,one state feedback controller and the other dynamic output feedback controller,are designed to ensure finitetime annular domain bounded of the closed-loop system.In addition,an algorithm is provided to deal with the obtained matrix inequalities.Finally,two examples are given to prove the validity of the results.(3)The problem of finite-time annular domain bounded control of nonlinear stochastic systems via neural network is studied.Firstly,the definition of the finite-time annular domain bounded is given,as well as some lemmas are given.Secondly,the state feedback finite-time annular bounded controller is designed to ensure the finite-time annular domain bounded of the closed-loop system.In addition,an algorithm is provided to deal with the obtained matrix inequalities.Finally,an example is given to prove the validity of the results.(4)The problem of finite-time annular domain bounded control of nonlinear stochastic poisson systems.Firstly,the definition of the finite-time annular domain bounded of the system and some lemmas are given.Secondly,the state feedback finitetime annular bounded controller is designed to ensure the finite-time annular domain bounded of the closed-loop system.In addition,an algorithm is provided to deal with the obtained matrix inequalities.Finally,an example is given to prove the validity of the results.