Robust stabilization of discrete-time uncertain nonlinear systems

This paper applies a recent result on nonlinear H^∞-optimal control to give a necessary and sufficient condition for the existence of a state feedback controller which absolutely stabilizes a discrete-time uncertain nonlinear system with structured uncertainty. The class of uncertain systems being considered contain uncertainties which satisfy a certain sum constraint. This sum constraint is a nonlinear discrete-time version of the integral quadratic constraint uncertainty description. The main result is established by using a nonlinear S-procedure result, which enables the robust absolute stabilization problem to be converted into a equivalent nonlinear H ^∞-optimal control problem.