On the Global Stabilization of a Class of Nonlinear Singularly Perturbed Systems Using Nonlinear H-infinity Control Approach

In this paper, a stabilizing controller for a class of nonlinear singularly perturbed systems is designed by using nonlinear H-infinity control approach. Since the stability and L
₂
-gain of the uncertainty block does not depend on the perturbation parameter, it can be referred as a robust controller. Also, through two theorems, the local and global stabilization of the controlled system are proven. Design procedure is discussed. The proposed approach is used to design a stabilizing controller for the Lorenz system with some specific parameters. The controller can globally stabilize the Lorenz system, while the pervious methods presented for the nonlinear singularly perturbed systems can only stabilize it locally, or even are unable to stabilize it.