Control And Filtering For Singular Markovian Jump System With Time Delay

In actual industrial production, it is usual that some parts fault, parts parameters change under different environmental temperature and connections changes between the subsystems, as well as some abrupt disturbance inputs. So they will lead the whole system to change the structure and the parameter. This type of system is very suitable to be described by Markovian jump system. Markov jump system is able to describe many kinds of real systems in the actual production systems, for example, electrical system, power system, manufacturing system, etc. So a large number of researchers and engineers pay more attention to the research of the Markovian jump system. On the other hand, with the development of science and technology, people put forward higher requirements for industrial production tools, which specifically embody in the controlled object that is more large scale and more complex, so just only markovian jump system model can not meet the practical needs, it is of utmost urgency to solve the system model that can describe the controlled object or control process. It is in order to solve the actual needs, so more and more scholars and engineers pay more attentions to the research of the singular Markovian jump systems with time-delay. The research about the singular Markovian jump systems with time-delay has not only important theory but also more important practical significance.This thesis mainly studies three problems of the system stochastic stability analysis, stabilization problem and H_? filtering. The thesis' research objects mainly involve continuous singular Markovian jump systems with time-varying delay and discrete singular Markovian jump systems with constant delay. The thesis' s specific work is summarized as follows:The stability of the continuous singular Markovian jump systems with time-varying delay is studied and the stabilization controller is designed.Based on the small gain theorem, we can obtain the delay-dependent stochastic admissible condition of the system by choosing new stochastic Lyapunov function and input-output approach, and then based on this condition stabilization controller is designed.The H_? filtering of the singular Markovian jump systems with time-varying delay is studied. The filtering error system is obtained by designing linear filter and combining with the original system. Based on the small gain theorem, we can obtain the delay-dependent stochastic admissible condition of the filterting error system by choosing new stochastic Lyapunov function and input-output approach, and then respectively calculate the full-order and reduced-order linear filter parameters.The H_? filtering of the singular Markovian jump systems with constant time-delay is studied. The filtering error system is obtained by designing linear filter and combining with the original system. Based on the small gain theorem, we can obtain the delay-dependent stochastic admissible condition of the filterting error system by choosing new stochastic Lyapunov function and input-output approach, and then calculate the filter parameters.