For problems in control systems, F(s), the Laplace Transform of f(t), occurs as a ratio of two polynomials in ‘s’.
Generally, the highest power of ‘s’ in P(s) is greater than the highest power of ‘s’ in Q(s).
F(s) can be conveniently expressed in terms of its partial-fraction components.
where F1(s), F2(s), etc. are the partial fractions of F(s)
If F(s) involves distinct poles, only then it can be expanded into simple partial fractions as follows:
where ak (k = 1, ...