Robust H∞ control of discrete-time descriptor systems

This paper addresses the problem of robust H_∞ control design for uncertain polytopic-type linear discrete-time descriptor systems. First, a new version of the bounded real lemma which is tailored for control design is proposed. Then, applying the derived bounded real lemma, we have developed a method of designing a robust state feedback H_∞ controller based on an affine parameter-dependent Lyapunov function. The method does not require applying any coordinate transformation to the system state-space model and in the case of uncertainty-free systems the proposed design conditions turn out to be necessary and sufficient. The controller design involves solving strict bilinear matrix inequalities and to this end a convergent iterative procedure is proposed that involves iterating between two LMI problems, namely an H_∞ control synthesis and an H_∞ performance analysis. Numerical examples borrowed from the literature are presented to illustrate the effectiveness and fast convergence of the proposed iterative procedure.