Stability analysis of linear impulsive delay dynamical systems via looped-functionals

This article investigates the asymptotic stability of impulsive delay dynamical systems (IDDS) by using the Lyapunov-Krasovskii method and looped-functionals. The proposed conditions reduce the conservatism of the results found in the literature by allowing the functionals to grow during both the continuous dynamics and the discrete dynamics. Sufficient conditions for asymptotic stability in the form of linear matrix inequalities (LMI) are provided for the case of impulsive delay dynamical systems with linear and time-invariant (LTI) base systems (non-impulsive actions). Several numerical examples illustrate the effectiveness of the method.