Non-linear unity-feedback systems and Q-parametrization†

Abstract

This paper concerns non-linear systems, defines a new concept of stability the  stability, and extends to unity-feedback systems the technique of Q-parametrization introduced for linear system by Zames and developed by Desoer, Chen and Gustafson. We specify (i) a global parametrization of all controllers that -stabilize a given -stable non-linear plant, (ii) a parametrization of a class of controllers that stabilize an unstable non-linear plant, and (iii) necessary and sufficient conditions for a nonlinear controller to simultaneously stabilize two non-linear plants.