Stability of systems described by differential equations containing impulses

Abstract

The class of systems described by differential equations containing impulses is of interest because most models for biological neural nets belong in that category as well as most pulse frequency modulation systems. In this paper an extension of Liapunov's second method is presented which can be used for the investigation of the stability of such systems. This is obtained by introducing a positive definite function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V(x)</tex> , which decreases during the occurrence of an impulse and remains constant or decreases during the free motion of the system.