Robust H_∞ Control Of Uncertain Discrete Singular Systems With Time-Varying Delays

This paper is focused on the problems of designing a robust H_∞ state feedback controller which is delay-dependent robustly stable for uncertain discrete singular systems with time-varying delays. Consider uncertain discrete singular systems with time-varying delayswhere x(k) ∈Rⁿ is the state vector, u(k) ∈ R^m is the controlled input, w(k) ∈ l₁^q [0,∞) is the exogenous disturbance signal and z(k) ∈ R^p is the controlled output. The matrix E ∈ R^n×n and is assumed 0 d, B₁, B₂ and C₀ are known real constant matrices with appropriate dimensions, and Ï„(k) is a positive integer and satisfies 0 < Ï„₁ ≤ Ï„(k) ≤τ₂, where Ï„₁ and Ï„₂ are known positive integer. ΔA(k), Δ A₂(k), ΔB₁(k) and Δ B₂(k) are unknown matrices representing time-varying parameter uncertainties, and are assumed to be of the formwhere M, N_a, N_b1, N_b2 and N_d are known real constant matrices and F(·) ∈ R^i×j is an unknown time-varying matrix function satisfying...