Exponentially asymptotically stable dynamical systems

Abstract

In this paper we introduce the notion of exponential asymptotic stability (EAS) in dynamical systems. We show that if a dynamical system is EAS, then it has a unique equilibrium point. Furthermore, if an EAS discrete system is embedded in a continuous system, then the continuous system is also EAS. Analytic criteria are given for an autonomous differential system to be an EAS. We further show that, under mild conditions, the perturbed system is EAS if the original system is

AMS(MOS)::

• 58F
• 34C
• 54H