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

2022 ◽  
pp. 199-220
Author(s):  
Rafał Stanisławski ◽  
Marek Rydel ◽  
Krzysztof J. Latawiec
Keyword(s):  
Model Reduction ◽  
Fractional Order ◽  
Discrete Time ◽  
Balanced Truncation ◽  
Fractional Order Systems

scholarly journals Balanced Truncation Model Order Reduction in Limited Frequency and Time Intervals for Discrete-Time Commensurate Fractional-Order Systems

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 258
Author(s):  
Marek Rydel ◽  
Rafał Stanisławski ◽  
Krzysztof Latawiec
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Model Order Reduction ◽  
Linear Time ◽  
Order Reduction ◽  
Balanced Truncation ◽  
Fractional Order Systems ◽  
Model Order ◽  
Reduction Techniques ◽  
Mathematical Formulas

In this paper we investigate an implementation of new model order reduction techniques to linear time-invariant discrete-time commensurate fractional-order state space systems to obtain lower dimensional fractional-order models. Since the models of physical systems correctly approximate the physical phenomena of the modeled systems for restricted time and frequency ranges only, a special attention is given to time- and frequency-limited balanced truncation and frequency-weighted methods. Mathematical formulas for calculation of the time- and frequency-limited, as well as frequency-weighted controllability and observability Gramians, are extended to fractional-order systems. An instructive simulation experiment corroborates the potential of the introduced methodology.

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