A new impulse inverse formula and it’s generalization including arbitrary input, are proposed. The new generalized inverse formula has the advantage of not being necessary to specify the first digital value of the input. Numerical instability of the inverse formula for arbitrary input is investigated carefully. An analysis of the perturbed stability and Lyapunov exponent are carried out. As the result of this analysis, it is shown that the estimated error is sensitive to the experimental error and previously estimated error as a sequential algorithm. Simulation using experimental data is also shown in the paper.