Abstract:

Finite-time stability was investigated for a class of generalized Hamiltonian systems with application to control design of nonlinear affine systems, and a number of new results were presented. Based on the structural properties of Hamiltonian systems and the existing results of local finitetime stability, several criteria were obtained for the finitetime stability of the class of generalized Hamiltonian systems. The obtained results were used to study the finitetime control design for a class of nonlinear affine systems. Via choosing a suitable Hamiltonian function, and utilizing the orthogonal decomposition Hamiltonian realization and the damping injection technique, a new control design procedure was established. Two illustrative examples were given to support the new results obtained in this paper.

Key words:  finite-time stability, Hamiltonian systems, damping injection, Hamiltonian realization