A review of time domain, frequency domain and stability analysis of linear complex-order systems

The main objective of this paper is to present the time domain, frequency domain and stability analysis of linear systems represented by differential equations with complex-order derivatives. The impulse and step response of three different complex-order systems have been presented numerically with the help of MATLAB. For frequency domain analysis, Bode-plots of the same three complex-order systems have been sketched. Complex-order systems have infinite numbers of complex-conjugate poles. The stability analysis of the complex-order systems has been done in two ways. Firstly, for systems to be stable, the complex-conjugate poles in the principle Riemann sheet must be in the left half plane. Secondly, the complex-order q = u + iv of the complex-order systems must be interior to an open disk in the u-v plane, for systems to be stable.