Impulse response of commensurate fractional-order systems: multiple complex poles

Abstract The impulse response of a fractional-order system with the transfer function $$s^{\delta }/{[(s^{\alpha }-a)^2+b^2]^n}$$ s δ / [ ( α - a ) 2 + b ] n , where $$n \in \mathbb {N}$$ ∈ N $$a {\mathbb {R}}$$ R $$b {R}}^+$$ $$\alpha $$\delta is derived via real and imaginary parts two-parameter Mittag-Leffler functions their derivatives. With aid robust algorithm for evaluating these derivatives, analytic formulas can be used an effective transient analysis systems multiple complex poles. By some numerical experiments it shown that this approach works well also when popular SPICE-family simulating programs fail to converge correct solution.