Researches On Stochastic System Control Problem

In the rapidly developing world, there are many phenomena occur randomly in real life,so it is necessary to analyze from the perspective of random and thinking. Markov jump system which is a special class of stochastic hybrid system, has draw more and more attention and been an attractive subject in the past several decades. The class of systems have been widely used in a large amount of physical systems as the normal system models can not reflect some of the physical systems, for example, the economic systems, biological systems,networked control systems or the power systems, etc.So far, a lot of interesting results have been reported in many papers of the systems with completely known transition probabilities matrix. But in real life, we can't fully know the transition probabilities matrix under normal circumstances, because there are many complexity of the system, uncontrollable natural factors and other reasons. Therefore,studying the systems with partly unknown transition probabilities has an significant theoretical value and a wide range of practical application.In this paper, we focus on the problem of finite-time filtering and non-fragile control for Markov jump singular systems with partially known transition probabilities. Contents of this paper as flowing.Firstly, we study the finite-time filtering control for Markovian jump singular systems with partially known transition probabilities. We can get the LMI conditions under applying Schur complement theorem and the definition of the finite-time filtering. A finite-time output feedback controller is also designed.Secondly, we study the H? finite-time filtering control for Markovian jump singular systems with partially known transition probabilities. We can get the LMI conditions under the definition of the H? finite-time filtering apply Schur complement theorem and the method of hand uncertainties. H? finite-time output feedback controller is also designed.Finally, we study the H? non-fragile control for Markovian jump singular systems with partially known transition probabilities. The LMI conditions under applying Schur complement theorem and the Dynkin formula. A H? non-fragile state feedback controller is also designed.