This paper addresses the stability problem of nonlinear systems with variable-time impulses. By Bequivalencemethod, we shall show that under the well-selected conditions each solution of the considered systemswill intersect each surface of discontinuity exactly once, and that the considered systems can be reduced to the fixedtimeimpulsive ones, which can be regarded as the comparison systems of the considered variable-time impulsivesystems. Based on the stability theory of fixed-time impulsive systems, we propose a set of stability criteria for thevariable-time impulsive systems. The theoretical results are illustrated by impulsive stabilization of Chua circuit.
This paper addresses the stability problem of nonlinear systems with variable-time impulses. By Bequivalencemethod, we shall show that under the well-selected conditions each solution of the considered systemswill intersect each surface of discontinuity exactly once, and that the considered systems can be reduced to the fixedtimeimpulsive ones, which can be regarded as the comparison systems of the considered variable-time impulsivesystems. Based on the stability theory of fixed-time impulsive systems, we propose a set of stability criteria for thevariable-time impulsive systems. The theoretical results are illustrated by impulsive stabilization of Chua circuit.