Worst case control for discrete-time systems in the presence of nonlinear uncertainties

This paper studies the problem of robust control of a class of uncertain discrete time systems, the cases of continuous-time and discrete-time systems. The class of uncertain systems is state model with linear nominal parts and norm-bounded nonlinear uncertainties in the state and output equations. We address the problem of robust H∞ control in which both robust stability and a prescribed H∞ performance are required to be achieved irrespectively of the uncertainties. It has been shown that instead of the nonlinear uncertain system, we may only consider a related linear uncertain system and thus, a linear static state feedback control law is designed, which is in terms of a Riccati inequality. An example is provided to show the potential of the proposed technique.