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. © 2014 EUCA.