An extension of Matrosov´s theorem with application to stabilization of nonholonomic control systems

We present a result on uniform attractivity of the origin for nonlinear time-varying systems. Our theorem generalizes Matrosov´s theorem which extends, in a certain manner, Krasovskii-LaSalle´s invariance principle to the case of general nonlinear time-varying systems. We show the utility of our theorem by analyzing uniform asymptotic stability of the origin for nonholonomic: systems in closed loop with particular smooth time-varying feedbacks previously proposed in the literature.