Robust non-fragile ℋ∞ control with regional pole location of discrete-time systems with multiple delays in the state

The problem of robust and non-fragile control by static state feedback gains assuring both the ℋ_∞ guaranteed cost and regional pole location of the closed loop eigenvalues is proposed in this paper, for uncertain discrete-time system with multiple delays in the states. The regional pole location, or the D-stabilization, concerns with the problem of locating the closed-loop system eigenvalues inside a circular region of the complex plane, called D(α, r)-region, with center in (-α, 0) and radius r. Besides this performance specification, the robust control gains are designed assuring an ℋ_∞ guaranteed cost between an exogenous input and the output signals. An iterative algorithm is proposed to solve the conditions achieving better results than previous results in the literature. The robust gains that feedback the delayed states are designed in a non-fragile way. Contrary to the most of the approaches presented in the literature, it is possible to prescribe an explicit percentage of perturbation for elements of these gains. A numerical design example is given to show the effectiveness of the proposed conditions.