Impulsive Stabilizability of Autonomous Systems

This paper introduces the concept of impulsive stabilization of a state which may not be an equilibrium point of the system. Both necessary and sufficient conditions are obtained by using the notion of an impulsive invariant set and the method of Lyapunov functions. These results are applied to stabilize an inverted pendulum and a three-species population growth model. In this population growth model, it is shown that by impulsively regulating one species the population of all three species can be maintained at a positive level, which otherwise would drop to a level of extinction for one of the species. Finally, the drug administration problem is discussed and it is shown that a set of desired drug concentration levels in a patient′s bloodstream can be impulsively stabilized by administering the drug orally at different time intervals.