Balanced Truncation Model Reduction in Approximation of Nabla Difference-Based Discrete-Time Fractional-Order Systems

This chapter surveys new results in applying Balanced Truncation (BT) model reduction methods to approximate LTI discrete-time noncommensurate fractional-order systems. For the fractional-order difference, the nabla-difference-based fractional-order difference under Grünwald–Letnikov definition is used. The method employs the Fourier-based decomposition of the fractional-order system and the BT model order reduction method. The presented algorithm’s main advantage is the specific representation of the fractional-order system enabling a simple, analytical formula for the determination of the Gramians. This contributes to a significant improvement of the computational efficiency of the BT reduction method. The simulation experiments confirm the introduced method’s effectiveness in terms of high modeling accuracy and low computational cost.