Robust passivity and control of nonlinear systems with structural uncertainty

This paper addresses several important issues including robust passivity, feedback equivalence, and the global stabilization, for a class of nonlinear systems with structural uncertainty. A robust version of the Kalman-Yacubovitch-Popov Lemma is derived, which provides a necessary and sufficient condition for an uncertain nonlinear system to be robust passive (resp. strictly robust passive). The robust KYP Lemma thus obtained enables us to build a feedback equivalence relationship between uncertain minimum-phase nonlinear systems having relative degree 1 and robust passive systems. The power of the feedback equivalence theorem is illustrated by solving the problems of global robust stabilization, for two classes of uncertain nonlinear systems. The global stabilization results developed in this paper neither require matching condition nor constraint the growth of the structural uncertainties.