November 1991 | Christopher I. Byrnes, Fellow, IEEE, Alberto Isidori, Fellow, IEEE, and Jan C. Willems, Fellow, IEEE
This paper addresses the conditions under which a nonlinear system can be rendered passive via smooth state feedback. It is shown that this is possible if and only if the system has relative degree 1 and is weakly minimum phase. The paper also proves that weakly minimum phase nonlinear systems with relative degree 1 can be globally asymptotically stabilized by smooth state feedback, provided certain controllability-like rank conditions are met. These results extend and incorporate several stabilization schemes proposed in the literature for global asymptotic stabilization of certain classes of nonlinear systems. The paper discusses dissipative and passive systems, stabilization by output feedback, and feedback equivalence to a passive system, providing a comprehensive analysis of these concepts and their implications for nonlinear control systems.This paper addresses the conditions under which a nonlinear system can be rendered passive via smooth state feedback. It is shown that this is possible if and only if the system has relative degree 1 and is weakly minimum phase. The paper also proves that weakly minimum phase nonlinear systems with relative degree 1 can be globally asymptotically stabilized by smooth state feedback, provided certain controllability-like rank conditions are met. These results extend and incorporate several stabilization schemes proposed in the literature for global asymptotic stabilization of certain classes of nonlinear systems. The paper discusses dissipative and passive systems, stabilization by output feedback, and feedback equivalence to a passive system, providing a comprehensive analysis of these concepts and their implications for nonlinear control systems.