Stabilizability of linear impulsive systems

This paper investigates the stabilizability of linear impulsive systems. The fact that some linear impulsive systems may be asymptotically stabilizable even though they are not stable under any consistent impulsive law is indicated by a numerical example. A sufficient condition for the asymptotical stabilizability of linear impulsive systems is presented and then the state-dependent impulsive law to stabilize linear impulsive systems is designed. A numerical example is introduced to illustrate the correctness and effectiveness of our proposed theoretical results.