aDepartment of Engineering, Australian National University, Canberra, ACT 0200, Australia;bSchool of Electrical Engineering, Australian Defence Force Academy, Canberra, ACT 2600, Australia
Abstract:
In the theory of linear H∞ control, the strict bounded real lemma plays a critical role because it provides a connection between the stabilizing solutions to the H∞ Riccati equations and the stability and disturbance attenuation of the closed-loop system. Nonlinear versions of the strict bounded real lemma are also important in nonlinear H∞ control theory. In this paper, we investigate the extension of the linear strict bounded real lemma and its smooth nonlinear generalization to cases where the solutions of the associated nonlinear PDE are not necessarily differentiable.