Robust H∞ controller designs for linear uncertain discrete-time systems: the LMI approach

In this paper, robust H_∞ control problem is investigated for a class of uncertain linear discrete-time systems with norm-bounded nonlinear uncertainties. The class of systems can be treated as linear nominal parts with nonlinear perturbations on both states and control inputs. By means of linear matrix inequality technique, an approach has been developed to find the tolerable uncertainty bounds for the robust H_∞ performance, and the corresponding static (or dynamic) output feedback controllers at the same time.