Robust control of discrete time uncertain dynamical systems

This paper is concerned with the problem of robust control of a class of discrete time systems with parameter uncertainty and unknown nonlinearities. The parameter uncertainty we consider is real time-varying norm-bounded and appears in both the state and output equations. We address the problem of designing linear dynamic output feedback controllers to achieve both robust stability and robust performance in an H∞ sense. Both the cases of finite and infinite horizon are considered. A technique is proposed for solving the above problems in terms of ‘scaled’ H∞ syntheses which do not involve parameter uncertainty and nonlinearities.