Some Remarks on Interconnection and Damping Assignment Passivity–Based Control of Mechanical Systems


aG.Viola1, Banavar, bJ. A. Acosta2 and c aA. Astolfi

image L2S, Supelec, Plateau du Moulon, 91192 Gif-sur-Yvette, France (

a Dipartimento di Informatica, Sistemi e Produzione, Università di Roma, Italy (astolfi(viola)

image Systems and Control Engineering, I. I. T. - Bombay, 101 A, ACRE Building Powai, Mumbai, 400 076, India (

b Depto. de Ingeniería de Sistemas y Automática, Escuela Superior de Ingenieros, Camino de los Descubrimientos s/n., 41092 Sevilla, Spain (

c Electrical Engineering Department, Imperial College, London, UK (

ABSTRACT. Total Energy Shaping is a controller design methodology that achieves (asymptotic) stabilization of mechanical systems endowing the closed–loop system with a Lagrangian or Hamiltonian structure with a desired energy function that qualifies as Lyapunov function for the desired equilibrium. The success of the method relies on the possibility of solving two PDEs which identify the kinetic and potential energy functions that can be assigned to the closed– loop. Particularly troublesome is the PDE associated to the kinetic energy which is nonlinear and non–homogeneous ...

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