The well-known Bounded Real Lemma plays a key role in ℒ2-gain based control methods such as H∞ control for both linear and nonlinear systems. Recently, conventional (linear) ℒ2-gain concepts have been generalized to the nonlinear ℒ2 framework to encompass a larger class of systems. A bounded real lemma has been developed corresponding to this generalized notion of nonlinear ℒ2-gain.
49th IEEE Conference on Decision and Control (CDC 2010). Proceedings of the 49th IEEE Conference on Decision and Control (Atlanta, GA 15-17 December, 2010) p. 2729 - 2734