Instability and unboundedness analysis for impulsive differential systems with applications to Lurie control systems

The present paper is dealt with the problem of the instability and unboundedness of impulsive differential systems. Numerous impulsive control systems were reported in the literature. The existing results give sufficient conditions for stability or boundedness of the system. If a system fails such conditions, it might be stable or unstable, bounded or unbounded. The most dangerous among these possible cases are unstable and unbounded ones. To our best knowledge, no criterion is available now to check these two cases. Thus, this paper presents some sufficient conditions on instability and unboundedness of impulsive systems, specializes them to Lurie control systems, and validates them with three illustrative examples.