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New trajectory-based small-gain results are obtained for nonlinear feedbacksystems under relaxed assumptions. Specifically, during a transient period, thesolutions of the feedback system may not satisfy some key inequalities thatprevious small-gain results usually utilize to prove stability properties. Theresults allow the application of the small-gain perspective to various systemswhich satisfy less demanding stability notions than the Input-to-OutputStability property. The robust global feedback stabilization problem of anuncertain time-delayed chemostat model is solved by means of thetrajectory-based small-gain results.

New Results in Trajectory-Based Small-Gain with Application to the Stabilization of a Chemostat