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

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