Robust D-stabilization with minimization of the ‛∞-guaranteed cost for uncertain discrete-time systems with multiple delays in the state

In this paper, a convex optimization problem for the stabilization of uncertain discrete-time system with multiple delays in the states is proposed. The presented conditions are sufficient for design robust state feedback gains such that the closed-loop system i) has eigenvalues located inside a circular region of the complex plane, called D(α,r)-region, with center in (-α,0) and radius r; and ii) achieves an H
_∞
guaranteed cost between an exogenous input and the output signals. It is possible to design robust controllers that feedback only the current state or also their past values. Numerical examples are provide to compare the proposed conditions with some literature results.