Finite-frequency model order reduction of discrete-time linear time-delayed systems

2015 ◽  
Vol 83 (4) ◽  
pp. 2485-2496 ◽  
Author(s):  
Xin Du ◽  
Feibing Fan ◽  
Da-Wei Ding ◽  
Fuwei Liu
Keyword(s):  
Discrete Time ◽  
Model Order Reduction ◽  
Linear Time ◽  
Order Reduction ◽  
Finite Frequency ◽  
Frequency Model ◽  
Model Order ◽  
Delayed Systems ◽  
Time Linear

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.

scholarly journals AN ITERATIVE MODEL ORDER REDUCTION METHOD FOR LARGE-SCALE DYNAMICAL SYSTEMS

2017 ◽  
Vol 59 (1) ◽  
pp. 115-133
Author(s):  
K. MOHAMED ◽  
A. MEHDI ◽  
M. ABDELKADER
Keyword(s):  
Dynamical Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Reduction Method ◽  
Linear Time ◽  
Order Reduction ◽  
Lyapunov Equation ◽  
Model Order ◽  
Iterative Model ◽  
Order Reduction Method

We present a new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach. This method is an extension of the SVD-rational Krylov method. It is based on two-sided projections: the SVD side depends on the observability Gramian by the resolution of the Lyapunov equation, and the Krylov side is generated by the adaptive-order rational Arnoldi based on moment matching. The use of the SVD provides stability for the reduced system, and the use of the AORA method provides numerical efficiency and a relative lower computation complexity. The reduced model obtained is asymptotically stable and minimizes the error ($H_{2}$and$H_{\infty }$) between the original and the reduced system. Two examples are given to study the performance of the proposed approach.

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