Output-Feedback Delay-Dependent Robust Stability And Stabilization For Uncertain Discrete-Time Singular Systems With Time-Delay

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)∈Rⁿ 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 ] = E₁F_k [ F₁ F₂ F₃ ] (2) Where E₁ ,F₁, F₂ and F₃ 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.