H_∞ control of linear discrete-time systems with norm-bounded nonlinear uncertainties

Robust H_∞ control of a class of discret-time uncertain systems is discussed which contains linear nominal parts and norm-bounded nonlinear uncertainties in both state and output equations. Such systems have a unique characteristic, that is, the two norm-bounded nonlinear uncertainties have the equivalent representation by means of time-varying and norm-bounded linear uncertainties. 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, it is obtained 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.