Stability of Nonlinear Systems with Variable-time Impulses: B-equivalence Method
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2017, Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany. This paper addresses the stability problem of nonlinear systems with variable-time impulses. By B-equivalence method, we shall show that under the well-selected conditions each solution of the considered systems will intersect each surface of discontinuity exactly once, and that the considered systems can be reduced to the fixed-time impulsive ones, which can be regarded as the comparison systems of the considered variable-time impulsive systems. Based on the stability theory of fixed-time impulsive systems, we propose a set of stability criteria for the variable-time impulsive systems. The theoretical results are illustrated by impulsive stabilization of Chua circuit.