Robust H∞ State-Feedback Design for Discrete-Time Descriptor Systems⁎

This paper deals with the design of robust H2 controllers for discrete-time descriptor systems with uncertain time-varying parameters in all state space matrices. It is assumed that the system matrices are affine functions of uncertain bounded parameters with bounded variations. Firstly, a novel version of the Bound Real Lemma for linear discrete time varying descriptor systems is presented. Then, the latter result is specialized for state-feedback design in terms of linear matrix inequality constraints in order to ensure the closed-loop admissibility while guaranteeing an upper-bound on the system H2-norm for all admissible uncertainty. Numerical examples are presented to illustrate the proposed control design technique. © 2018