A connection between H^∞ control and the absolute stabilizability of uncertain systems

This paper considers a stabilization problem for a class of uncertain systems in which the uncertainty satisfies a certain integral quadratic constraint. Such uncertain systems have been previously studied in the theory of absolute stability, with most publications in this area being in the Russian literature. The paper introduces a notion of absolute stabilizability and shows that an uncertain system is absolutely stabilizable if and only if there exists a solution to a corresponding H^∞ control problem. The paper also shows that if an uncertain system can be absolutely stabilized via nonlinear output feedback control then it can be absolutely stabilized via linear output feedback control.