Simultaneous Stabilization of a Collection of Port-controlled Hamiltonian Systems with Application to Affine Nonlinear Systems

This paper investigates the simultaneous stabilization of a collection of nonlinear port-controlled Hamiltonian (PCH) systems, and proposes several new results on the design of simultaneous stabilization controllers for the PCH systems. Using the dissipative Hamiltonian structural properties, the collection of PCH systems are combined to generate an augmented PCH system, with which a simultaneous stabilization controller is then designed. Based on the zero-state detectability, a more general result is also obtained for the simultaneous stabilization of the PCH systems. Finally, using the results obtained in this paper, the simultaneous stabilization of a collection of affine nonlinear systems is also investigated, and some useful corollaries are presented.