AN ENERGY-BASED DERIVATION OF LYAPUNOV FUNCTIONS FOR FORCED SYSTEMS WITH APPLICATION TO STABILIZING CONTROL

摘要

In this paper we show how the Hamiltonian formulation of systems may be used in order to derive Lyapunov functions for forced systems with constant input In a first part the structure of Hamiltonian systems with dissipation is recalled and it is shown that, under certain integrability assumptions on the input vector fields, a candidate Lyapunov function for the forced system may be derived. In a second part, an interpretation of this candidate Lyapunov function is given in terms of the total energy of the forced system, composed of the sum of its internal energy and the energy function associated with the source element. In the third part, such a candidate Lyapunov function is used to derive a stabilizing controller for the boost converter.