This paper consider the problem of designing a robust stabilizing and output feedback controller for uncertain time-delay discrete-time singular system. Consider the uncertain time-delay discrete-time singular system described byWhere x(k)∈R^{n} is the state variable, u(k)∈R^{m} is the control input, y(k)∈R^{p} is the measured output,d is the unknown constant integer time-delay,and 0 < d < (?), (?) > 0 is the known integer.The matrix E∈R^{n*n} is singular and rankE = r < n, A∈R^{n*n}, B∈R^{n*n},Ad∈R^{n*n} and C are real constant matrices,△A,△Ad and△Bare norm-bounded uncertain parameter matrices,,and are assumed to be of the following form[△A△A_{d}△B ] = E_{1}F_{k} [ F_{1} F_{2} F_{3} ] (2) Where E_{1} ,F_{1}, F_{2} and F_{3} are known constant matrices with appropriate dimensins, F_{k}∈R^{α*β} are unknown matrix satisfying F_{k}^{T} F_{k}≤I (3)Throughout this paper ,our purpose is to design a static controllerand a dynamic controller∑_{c}: (?)such that the closed-loop system formed by system (1) and the controllers is admissible for all uncertainties satisfying (2)and (3).First, we consider the system without the exogenous disturbance signal,when E in the system (4) is nonsingular ,Theorem 1 gives sufficient LMI condition such that the nominal unforced singular time-delay system of system (1) is admissible ;then the robust output feedback controller is discussed based on similar method , and LMI condition is obtained.Theorem 4 gives the LMI condition that there exist a static controller such that the closed system is admissible ,and the method of designing the static controller.Theorem 5 gives the LMI condition that there exist a dynamic controller such that the closed system is admissible ,and the method of designing the dynamic controller.at last we illustrate the validity of the result provided in this paper with a numerical example. |