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Partial fraction expansion is a technique that allows finding the inverse of the Laplace transform of rational functions, i.e., functions represented as the quotient of two polynomials. The essence of this technique involves decomposing a rational function into the sum of simpler terms for which the Laplace transform is known.

Partial fraction expansion in Matlab:

Syntax:

[r, p, k] = residue(num, den)

The residue function takes as arguments the numerator and denominator of the rational function expressed as vectors, with their elements being the coefficients of the respective polynomials.

The function's result is assigned to the variables r (the residue), p (poles), K (a vector representing the coefficients of a polynomial in terms of s when the numerator's degree is greater than the denominator's).