Stability Analysis And Control For Stochastic Systems Driven By Poisson Processes And Wiener Processes

Since systems in the real world are always perturbed by stochastic noises,stochastic systems have already attracted researchers’ attention,and some results about stochastic systems have been presented.In the most of results on stochastic systems,stochastic noises are described by Wiener processes.However,stochastic noises in the practice are complex,and systems are often perturbed by continuous and jump stochastic phenomena simultaneously.Note that Wiener process can describe continuous stochastic phenomena rather than jump stochastic phenomena,Poisson jump process should be introduced to model jump stochastic disturbances.Due to above reason,this dissertation is concerned with the stability analysis,stabilization and guaranteed cost control problems for stochastic systems driven by Poisson processes and Wiener processes.1.The stability problem for stochastic systems driven by Poisson processes and Wiener processes is considered.By using the knowledge of stochastic analysis and introducing the Doob-Meyer decomposition for Poisson process,this paper presents an approach to transform the expectation of stochastic integral with respect to Poisson process into the expectation of Lebesgue integral.On basis of this,this paper utilize Lyapunov theory and Measure theory to present a simple but effective stability criteria.2.Based on the stability analysis,this dissertation investigates the stabilization problem for stochastic systems driven by Poisson Processes and Wiener processes.By Lyapunov stability theory,stochastic analysis and measure theory,this paper designs a state feedback controller such that the corresponding closed-loop system is stochastically stable.And a numerical example is given to show the effectiveness of the proposed approach.3.Then,this dissertation investigates the guaranteed cost control problem for uncertain stochastic systems driven by Poisson Processes and Wiener processes.Making use of the knowledge of Lyapunov stability theory,stochastic analysis and measure theory,this paper designs a state feedback controller such that the corresponding closed-loop system is robustly stochastically stable and a specified quadratic cost function has an upper bound for all admissible uncertainties.And a numerical example is given to show the effectiveness of the proposed approach.