Model Order Reduction of Linear Systems via the Cross Gramian and SVD

2019 ◽  
Vol 66 (3) ◽  
pp. 422-426 ◽  
Author(s):  
Yao-Lin Jiang ◽  
Zhen-Zhong Qi ◽  
Ping Yang
Keyword(s):  
Linear Systems ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Model Order ◽  
The Cross

scholarly journals Reduced Order Controller Design for Symmetric, Non-Symmetric and Unstable Systems Using Extended Cross-Gramian

Machines ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 48 ◽  
Author(s):  
Azhar ◽  
Zulfiqar ◽  
Liaquat ◽  
Kumar
Keyword(s):  
Model Order Reduction ◽  
Controller Design ◽  
Order Reduction ◽  
Original System ◽  
Computational Effort ◽  
Model Order ◽  
Unstable Systems ◽  
Reduced Order ◽  
The Cross ◽  
Symmetric Systems

In model order reduction and system theory, the cross-gramian is widely applicable. The cross-gramian based model order reduction techniques have the advantage over conventional balanced truncation that it is computationally less complex, while providing a unique relationship with the Hankel singular values of the original system at the same time. This basic property of cross-gramian holds true for all symmetric systems. However, for non-square and non-symmetric dynamical systems, the standard cross-gramian does not satisfy this property. Hence, alternate approaches need to be developed for its evaluation. In this paper, a generalized frequency-weighted cross-gramian-based controller reduction algorithm is presented, which is applicable to both symmetric and non-symmetric systems. The proposed algorithm is also applicable to unstable systems even if they have poles of opposite polarities and equal magnitudes. The proposed technique produces an accurate approximation of the reduced order model in the desired frequency region with a reduced computational effort. A lower order controller can be designed using the proposed technique, which ensures closed-loop stability and performance with the original full order plant. Numerical examples provide evidence of the efficacy of the proposed technique.

Model order-reduction for discrete-time switched linear systems

2012 ◽  
Vol 43 (9) ◽  
pp. 1753-1763 ◽  
Author(s):  
Abderazik Birouche ◽  
Benjamin Mourllion ◽  
Michel Basset
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Model Order ◽  
Switched Linear Systems

Singular perturbation approximation for linear systems with Lévy noise

2018 ◽  
Vol 18 (04) ◽  
pp. 1850033 ◽  
Author(s):  
Martin Redmann ◽  
Peter Benner
Keyword(s):  
Singular Perturbation ◽  
Linear Systems ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Reduction Technique ◽  
Lévy Noise ◽  
Model Order ◽  
Linear Evolution Equation ◽  
Levy Noise ◽  
Perturbation Approximation

To solve a stochastic linear evolution equation numerically, finite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear equations of high order. To reduce the high dimension for practical computations, we consider the singular perturbation approximation as a model order reduction technique in this paper. This approach is well-known from deterministic control theory and here we generalize it for controlled linear systems with Lévy noise. Additionally, we discuss properties of the reduced order model, provide an error bound, and give some examples to demonstrate the quality of this model order reduction technique.

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