On Stabilization of Delayed Linear Singular Systems via Impulsive Control

This paper is concerned with the stability problem of a class of delayed linear singular systems based on impulsive control. The key idea is to develop two novel Lyapunov methods to effectively deal with two different cases of delays: fast time-varying delay and slow time-vary delay. These Lyapunov methods take good advantage of the hybrid structure characteristics of the impulsively controlled singular systems so as to establish exponential stability of the underlying singular systems. A convex technique is applied to represent the derived stability conditions within the linear matrix inequalities framework, which facilitates design of the desired impulsive controllers. An illustrative example is given to substantiate the efficiency of the developed exponential impulsive stabilization conditions.