Frequency weighted model reduction in approximation of nabla difference-based discrete-time fractional-order systems

Abstract

The article presents new results in terms of Frequency Weighted (FW) model reduction method in application to approximate LTI discrete-time non-commensurate fractional-order systems based on the Grunwald-Letnikov nabla fractional-order difference. The method applies the Fourier-based decomposition of the system and the FW model order reduction method. The main advantage of the proposed modeling approach is the specific representation of the fractional-order system enabling a simple, analytical formula for the determination of the Gramians. This significantly improves the computational efficiency of the proposed FW reduction method. The simulation experiments confirm the low computational effort of the introduced processing and its high modeling accuracy