$H_{\infty}$ Control of Nonlinear Singular Hamiltonian Systems with Actuator Saturation *

The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> control problem of Hamiltonian systems which have actuator saturation is studied in this paper and some results are given. At the beginning the system will be molded into strictly dissipative Hamiltonian form using non-singular transformations and appropriate state feedback. Next the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> controller is designed to build on this form and is eventually applied to the initial system. Finally, an electric circuit with actuator saturation is given which is a nonlinear singular system, and stabilization of the electric circuit is accomplished using the controller shown in the note.