Finite-time stabilization and H∞H∞ control for a class of nonlinear Hamiltonian descriptor systems with application to affine nonlinear descriptor systems

This paper studies the finite-time stabilization and finite-time H∞H∞ control problems of a class of nonlinear Hamiltonian descriptor systems with applications to affine nonlinear descriptor systems. Via an appropriate state feedback, an equivalent nonlinear dissipative Hamiltonian differential-algebraic system is first obtained. With the obtained dissipative form, a finite-time stabilization control design procedure is then presented, based on which a finite-time H∞H∞ controller is designed for the system with external disturbances. Finally, the obtained results for Hamiltonian descriptor systems are applied to affine nonlinear descriptor systems. Simulation results on nonlinear circuit system show the effectiveness of the controllers proposed in this paper.