On robust stabilization of delayed impulsive systems subject to parametric uncertainties

Impulsive systems allowing for certain instantaneous changes of the system state in addition to continuous dynamics are instrumental in describing a number of real-world applications. This paper is devoted to study of robust stability and robust stabilization of delayed impulsive systems subject to parametric uncertainties. The impulsive systems under study are classified into three types in terms of combinations of continuous dynamics with impulsive effects, namely, (1) stable continuous dynamics combined with destabilizing impulsive effects, (2) stabilizing continuous dynamics combined with stabilizing impulsive effects, and (3)unstable continuous dynamics combined with stabilizing impulsive effects. Under the assumption of time-varying but norm-bounded parametric uncertainties, Lyapunov function and Razumikhin-type techniques are applied to establish delay-independent sufficient conditions for the problems of robust stability and robust stabilization of impulsive systems. These stability criteria expressed in linear matrix inequalities are readily checkable. The usefulness of the theoretical findings is validated by numerical results.