On finite-time stability and stabilization of nonlinear port-controlled Hamiltonian systems

Abstract

The finite-time stability and stabilization of nonlinear port-controlled Hamiltonian (PCH) systems are investigated in this paper, and a number of new results are proposed. Firstly, by exploiting the Hamiltonian structural properties, a proper form of the Hamiltonian function is obtained, based on which a finite-time stability criterion is then presented for a class of Hamiltonian systems. Secondly, using the obtained stability criterion and the so-called "energy shaping plus damping injection" technique, the continuous finite-time stabilization problem is studied for the PCH system, and several global stabilization results are provided. Finally, the continuous robust finite-time stabilization of the PCH system with external disturbances is investigated, and two results on designing global robust finite-time stabilizers are obtained. Study of several examples with numerical simulations shows that the control design approach developed in this paper works very well. © 2012 Science China Press and Springer-Verlag Berlin Heidelberg.