Some recent results of analysis and control for impulsive systems

Abstract Since impulsive control has less conservation in the analysis of dynamical behaviors, a surge of attention has been paid on the study of impulsive control systems. This paper is dedicated to review some recent developments of impulsive control theory. Some fundamental theory on impulsive control systems and some very recent interesting results are reviewed and addressed. Based on the characteristics of impulsive control systems, we summarize three fundamental factors for the design of impulsive controllers, namely, the impulsive strength, the impulsive frequency and the impulsive instant. Then a systematic account of useful stability analysis methods are introduced, and these methods provide researchers a well-organized tool box to learn the impulsive control systems. Moreover, as a vital aspect, the effects of delays on impulsive systems are discussed. Finally, some potential developments and further work on impulsive control systems are briefly presented and discussed.