STABILITY OF NONLINEAR SYSTEMS via BELLMAN-GRONWALL LEMMA.

Abstract

Governing equation of a system with a linear element and a nonlineir time varying gain can be expressed in an integral equation form. Bellman-Gronwall Lemma can be applied to this integrti equation to derive bounied-input-baunded-output stability and Liapunw stability.The criterion derived ieads to less con     servative results, compared with other methods, such as circl criterion, for cases where the fluctuations in the gain are large and rapid. This is so because in the new criterion the gain appears in the arg merit of a time integral, which significantly reduces the effect or fluctuations.