Analysis And Control For A Class Of Singular Stochastic Systems With It(?)-type

As an emerging new research field,control of singular stochastic systems is very challenging.Based on singular systems analysis method and stochastic stability theory,Ito formula,singular systems linear transformation,generalized inverse matrix,linear matrix inequality(LMI)and generalized Riccati equation are employed to study stability analysis and controller designs of singular stochastic systems in this dissertation.Furthermore,stability analysis and controller designs of uncertain singular stochastic systems,fuzzy singular stochastic systems and singular stochastic bio-economic systems are discussed.Meanwhile,the optimal control problem of singular stochastic systems is investigated.The main contributions of this dissertation are summarized as follows.(1)The finite-time H? control problem of singular stochastic systems is investigated.The finite-time stability definition of singular stochastic systems is given and the finite-time stability criterion for such systems is obtained.A state feedback controller is designed,which can guarantee the corresponding closed-loop system has H? performance.Then,the robust finite-time H? control problem of uncertain singular stochastic systems is studied.The designed controllers guarantee the finite-time stability and the H? performance of closed-loop systems.The results of the simulation examples demonstrate the correctness and effectiveness of the proposed method.(2)The finite-time H? control problem of fuzzy singular stochastic systems is discussed.Aiming to analyze nonlinear singular stochastic systems,T-S fuzzy model is introduced.Based on T-S fuzzy method,fuzzy singular stochastic systems are established.According to the finite-time stability theory,several finite-time stability criteria are obtained and controller designs are given.A fuzzy state feedback controller is designed,which can guarantee the corresponding closed-loop system is finite-time stochastically stable and has H? performance.Then,the robust finite-time H? control problem of uncertain fuzzy singular stochastic systems is studied.The H? controller design method is obtained by the finite-time stability conclusions of singular stochastic systems.The results of the simulation examples verify the correctness and effectiveness of the proposed method.(3)The problem of finite-time fuzzy control for singular stochastic bio-economic systems is investigated.In order to analyze nonlinear singular bio-economic systems,T-S fuzzy method is utilized.A fuzzy state feedback controller is designed such that the singular bio-economic system is finite-time stable.Then,the finite-time fuzzy control problem for singular stochastic bio-economic systems with stochastic disturbance factors is discussed.The system is finite-time stochastically stable by the designed fuzzy state feedback controller.The results may present some new methods to ensure the finite-time stability of singular stochastic bio-economic systems.The bio-economic system simulation example of biological sardine of the Moroccan western coastline area is given to illustrate the effectiveness of the proposed method.(4)The control problem for T-S fuzzy singular stochastic systems based on non-quadratic Lyapunov function approach is investigated.Mean square admissibility conditions are given by the non-quadratic Lyapunov function approach.The method not only reduces the conservatism of the single Lyapunov function approach,but also avoids large amount of calculation of the fuzzy Lyapunov function approach and difficulty to get LMI form results.Moreover,the restrictive conditions on membership function derivative are relaxed.Then,based on parallel distributed compensation(PDC)and non-parallel distributed compensation(non-PDC),fuzzy controllers are designed.In the solving process,feasible regions of the corresponding LMIs are compared.The simulation examples have shown that the design method of the non-PDC fuzzy controller is less conservative and owns lower computational complexity.(5)The optimal control problem of singular stochastic systems is studied.The well-posedness condition of the solution for singular stochastic systems is proposed and a new mean square stability criterion of such systems is given as well.The finite-time horizon and infinite-time horizon linear quadratic regulator(LQR)problems for singular stochastic systems are presented by the generalized Riccati equations,respectively.The designed controllers guarantee the stability of such systems.A practical example about the optimal portfolio selection problem in the financial markets shows the effectiveness of our presented method.