A connection between H_∞ control and the absolute stabilizability of discrete-time uncertain linear systems

We consider the problem of stabilizing a class of uncertain discrete-time systems in which the uncertainty satisfies a certain sum constraint. We consider a notion of absolute Stabilizability for discrete-time systems and show that a necessary and sufficient condition for a discrete-time uncertain system to be absolutely stabilizable is existence of a solution to a corresponding discrete-time H_∞ control problem. We also show that if it is possible to stabilize an uncertain system via nonlinear output feedback control then it is possible to absolutely stabilize it via linear output feedback control.