Model reduction in commensurate fractional-order linear systems

Abstract

In this paper, some commonly used model reduction methods for integer-order systems are employed to approximate commensurate fractional-order linear systems. In comparison with the original system, the approximating model possesses a smaller inner dimension, while its fractional order is the same as that of the original system. The applied methods fall into the global reduction category, such as direct truncation and singular perturbation methods, and into the local reduction category, such as Pade approximation, partial realization, shifted Pade approximation, and rational interpolation methods. The applicability of these methods is illustrated by approximating a sample high-dimensional, commensurate, fractional-order, linear system.