Abstract
This primer article focuses on the representation of solutions and finite-time stability of impulsive first-order delay differential systems. We define delayed matrix function with impulses and use variation of parameters to obtain a representation of solutions of linear systems with impulse effects. The famous classical Grownwall inequalities and properties of delayed matrix exponential with impulses are used to develop sufficient conditions for finite-time stability. In the end, we provide some examples to support the results.
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