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$X_2(s)=-\sum_{i=0}^{h-1}N^is^i(N+U(s))$, where $N$ is nilpotent matrix of order $h$, Could anyone help me to understand inverse laplace transformation of $X_2(s)$? $\delta$ is dirac delta function.

Thanks for helping. I am attaching the actual expression. But I guess I will understand the original if I understand this one.

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