The states of many systems are partial measurable or incomplete measurable, therefore constructing observer even realizing feedback control by estimating state is a very meaningful research work. There are many works about the approach to design observer at present, however, it is less about the approach to design observer for a class of discrete control systems with time-delay especially a class of discrete singular control systems with time-delay. In this paper, a new approach for a class of discrete control systems with time-delay is discussed, the observer model is firstly given, and then the assumptions of the observer are investigated, the integrated algorithm to solve the unknown of observer is designed by the solution of Sylvester function and the condition of linear matrix inequality(LMI). Then we extend the new approach to a class of discrete singular control systems with time-delay, the observer model is firstly given, and then the assumptions of the observer are investigated, the integrated algorithm to solve the unknown of observer is designed by the solution of Sylvester function and the asymptotic stability criteria for a class of discrete singular control systems with time-delay.The paper is divided into five parts:The background of design observer is introduced in section 1.In section 2, the mathematical knowledge needed are introduced.In section 3, the observer model for a class of discrete control systems with time-delay is firstly given, and then the assumptions of the observer are investigated, the integrated algorithm to solve the unknown of observer is designed by the solution of Sylvester function and the condition of linear matrix inequality(LMI). Finally, an example is given to illustrate the feasibility of the method.In section 4, the observer model for a class of discrete singular control systems with time-delay is firstly given, and then the assumptions of the observer are investigated, the integrated algorithm to solve the unknown of observer is designed by the solution of Sylvester function and the asymptotic stability criteria for a class of discrete singular control systems with time-delay. Finally, we give an example to illustrate the feasibility of the method.The conclusions of this paper are summarized, and problems which need further research are put forward in section 5. |