A new small-gain theorem with an application to the stabilization of the chemostat

New small-gain results are obtained for nonlinear feedback systems under relaxed assumptions. Specifically, during a transient period, the solutions of the feedback system may not satisfy some key inequalities that previous small-gain results usually utilize to prove stability properties. The results allow the application of the small-gain perspective to various systems that satisfy less-demanding stability notions than the input-to-output stability property. The robust global feedback stabilization problem of an uncertain time-delayed chemostat model is solved by means of the new small-gain results. Copyright © 2011 John Wiley & Sons, Ltd.