Researchers from a variety of engineering fields are very eager to investigate fractional-order (FO) systems, as their mathematical models have proved to be more effective in depicting various physical phenomena such as electrochemical processes, long-distance lines, dielectric polarization, viscoelastic materials, coloured noise and even chaos. FO systems are fundamentally the approximations of the integer-order (IO) systems. The system dynamics of the FO systems include the non-integer differential or integral operators. It should be noted that the FO model reflects more reliable properties as compared to its IO model. However, the FO system is having infinite dimension. Thus, these infinite- order systems are approximated by finite integer-order rational models for the purpose of investigation, simulation and controller design. In system theory, model order reduction (MOR) is a method of reducing the complex large-scale structure to a much smaller number of variables. It is an important functional challenge as it simplifies the understanding of the system dynamics, reduces the computational burden of simulation and improves the design of controllers. MOR is an age-old practice in integer-order systems, but a limited amount of research has been done on fractional-order models. Mostly three types of FO systems are reported in the literature. They are respectively coined as commensurate, non-commensurate and fractional- order systems with non-rational powers. Commensurate type FO systems are those in which the non-integer powers of integrators and differentiators are multiple of real number and therefore such class of system can easily be transformed into IO system using simple assumptions. Non-commensurate FO systems involve non-integer terms which are not necessarily multiples of real numbers. Even FO systems with non-integer terms in the form of non-rational numbers also exist. Hence their analyses are not easy.
