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

The impulse response of a fractional-order system with the transfer function s(delta)/[(s(alpha) - a)(2) + b(2)](n), where n is an element of N, a is an element of R, b is an element of R+, alpha is an element of R+, delta is an element of 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.