Lyapounov stability for impulsive dynamical systems

Abstract

This article addresses the problem of stability of impulsive control systems whose dynamics are given by measure driven differential inclusions. One important feature concerns the adopted solution which allows the consideration of systems whose singular dynamics do not satisfy the so-called Frobenius condition. After extending the conventional notion of control Lyapounov pair for impulsive systems, some stability conditions of the Lyapounov type are given. Some conclusions follow the outline of the proof of the main result.