Observer Design For Discrete-time Singular Markov Jump Systems With Time-delay

The study of Markov jump systems is of both theoretical and practical im-portance. Therefore, much attention has been addressed to investigate Markov jump systems. Like other systems, we can improve the performance of Markov jump systems via the state feedback control. However, because of the limi-tation of reality, we can not get all the state variables of the control systems in many situations, that makes the state feedback control can not be realized. One important method to solve the problem is to construct the observers of the control systems.In this paper, observer design for discrete-time singular Markov jump systems with time-delay is considered. Sufficient conditions for existence of the observers are obtained via matrix rank conditions and the solution of linear matrix inequalities (LMIs). Functional observers and reduced order observers are discussed. There are two types of observers for functional observers and reduced order observers:observers with delay in state, observers without delay in state. The detailed design steps are also obtained. All observers in this paper is normal systems. That solves the problem of using the normal systems to asymptotically reconstruct the singular systems. Several numerical examples are given to illustrate the validity of the results. The paper contains the following three chapters:In Chapter 1, the research background and status of discrete-time singular Markov jump systems with time-delay are introduced, and some important achievements are reviewed. Moreover, the notations used in this paper are listed.In Chapter 2, functional observers are discussed. There are two types of observers for functional observers:functional observers with delay in state, functional observers without delay in state. Sufficient conditions and detailed design steps for both types of functional observers are obtained, respectively. Numerical examples are given to illustrate the validity of the results.In Chapter 3, reduced order observers are discussed. Sufficient conditions and detailed design steps for both reduced order observers with delay in state and reduced order observers without delay in state are obtained, respectively. Numerical examples are given to illustrate the validity of the results.