ROBUST STABILIZATION OF DISCRETE-TIME UNCERTAIN NONLINEAR-SYSTEMS

This paper applies a recent result on nonlinear H-infinity-optimal con trol to give a necessary and sufficient condition for the existence of a state feedback controller which absolutely stabilizes a discrete-ti me uncertain nonlinear system with structured uncertainty. The class o f uncertain systems being considered contain uncertainties which satis fy a certain sum constraint. This sum constraint is a nonlinear discre te-time version of the integral quadratic constraint uncertainty descr iption. The main result is established by using a nonlinear S-procedur e result, which enables the robust absolute stabilization problem to b e converted into a equivalent nonlinear H-infinity-optimal control pro blem.