A generalization of the bounded real lemma (Q1410713)

The bounded real lemma is a central tool in H\(^\infty\) control theory, that characterizes conditions under which a transfer function is contractive on the imaginary axis. The author presents several generalizations of the bounded real lemma, essentially by replacing the condition of being contractive by the condition of being bounded in absolute value (in the linear operator sense) by another transfer function on the imaginary axis. The characterization is done in terms of dissipation inequalities instead of the usual Riccati equations.