H_∞ Control of Linear Discrete‐Time Systems With Norm‐Bounded Nonlinear Uncertainties

Abstract

ABSTRACT In this paper, robust H ∞ control of a class of discrete‐time uncertain systems in state‐space form with linear nominal parts and norm‐bounded nonlinear uncertainties in both state and output equations is discussed. Such systems have a unique characterisic; that is, the two norm‐bounded nonlinear uncertainties have the equivalent representation by means of time‐varying and norm‐bounded linear uncertainties. To overcome the conservativenss of [5], the two nonlinear uncertainty sets are considered to be different. Then, by converting such systems into related discrete‐time linear systems with time‐varying and norm‐bounded linear uncertainties, we obtain that a sufficient condition for robust H ∞ control of such systems is equivalent to the solvability of the same problem of the related linear uncertain systems, which is solvable by means of a linear algebraic Riccati inequality.