In this article, we study the representation of solutions and exponential stability of nonlinear impulsive delay systems in the case of commutative matrices. Firstly, we study nonlinear single delay impulsive systems involving nonlinear term independent on time delay or depending on time delay. Secondly, we extend to study nonlinear multi-delayed impulsive systems involving nonlinear term independent on time delay or depending on time delay. By virtue of fundamental properties of delayed matrix exponential and impulsive Gronwall inequalities, many new interesting sufficient conditions to guarantee the trivial solution and nontrivial solutions are exponentially stable when time tend to infinite. Finally, numerical examples are demonstrated the validity of our theoretical results.

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