Filtering And Control For Nonlinear Stochastic Systems With Markovian Switching And Time-delays In Almost Surely Sense

In this thesis, the ?ltering and control problems for nonlinear stochastic systems with Markovian switching and time-delays are discussed. The content of this thesis is introduced from three parts. In the ?rst part, the problem of the stability for nonlinear stochastic systems with Markovian switching and time-delays is studied.Some su?cient conditions are derived for systems to be almost surely stable or almost surely exponentially stable. In the second part, in terms of the results of the ?rst part,the problems of the almost sure state estimation and the almost sure H∞?ltering are discussed. Finally, based on the results of previous parts, the problems of almost sure stabilization, the almost sure H∞control and robust slide mode almost sure H∞control are considered for nonlinear stochastic systems with Markovian switching and time-delays.Speci?cally, the frame of this thesis is given as follows:The problem of stability is investigated for nonlinear stochastic systems with Markovian switching and time-delays. Stability is a basic problem in the engineering design. Under the assumption that the nonlinear coe?cients in the drift part and in the di?usion part only satisfying local Lipschitz condition, some su?cient conditions are obtained for systems to be almost surely stable by means of the general It?o’ formula, the semimartingale convergence theorem, the Doob’s martingale inequality and Chebyshev’s inequality. Furthermore, the problem of stability in the almost surely exponentially sense is considered for nonlinear stochastic systems with Markovian switching and mode-dependent interval delays. Under the assumption that the nonlinear coe?cients satisfying global Lipschitz condition, some su?cient conditions are derived for systems to be almost surely exponentially stable based on Hamilton-Jacobi-Isaacs(HJI) inequalities, Burkholder-Davis-Gundy inequalities and Borel-Cantelli lemma.The problem of state estimation is studied for nonlinear stochastic systems with Markovian switching and time-delays. Under the assumption that the nonlinear coe?cients satisfying local Lipschitz condition but without a linear growth condition,by utilizing the stopping method combined with martingale inequalities, some su?-cient conditions are established under which the estimation process is almost surely asymptotically stable and the upper bound of estimation error is also determined.Furthermore, a suboptimal state estimator is obtained by solving an optimization problem in the H2 sense. And then, the almost sure H∞?ltering problem is handledfor nonlinear stochastic systems with Markovian switching and time-delays. Under the assumption that the nonlinear coe?cients satisfying global Lipschitz condition,based on the above results, some su?cient conditions are given to guarantee the desired H∞?lter to be designed in terms of HJI inequalities. Moreover, for a special class nonlinear stochastic systems with Markovian switching and time-delays, the design method of LMI is given to obtain the corresponding ?lter.The problems of stabilization and H∞control are discussed for nonlinear stochastic systems with Markovian switching and time-delays. By means of LMI approach,the almost sure state-feedback controller is designed for a special nonlinear stochastic systems with Markovian switching and time-delays. Then, the robust sliding mode almost sure H∞control problem is considered for nonlinear stochastic systems with Markovian switching and time-delays. The sliding mode controller is designed such that the statement of the system draw onto the speci?ed sliding surface with probability 1. Some su?cient conditions are derived to ensure the sliding mode surface to be robust almost surely exponentially stable with the H∞disturbance attenuation level performance. Finally, the problem of robust almost sure H∞control is studied for a special class of sampled-data nonlinear stochastic systems with Markovian switching and time-delays. Only two sampling periods are considered whose occurrence probabilities are constant and satisfying Bernoulli distribution. By converting probabilistic sampling into time-varying delays, the concerned systems are transformed into systems with time-delays. Some su?cient conditions are derived to guarantee the closed systems to be almost surely exponentially stable with the H∞disturbance attenuation level performance.