Truncated model reduction methods for linear time-invariant systems via eigenvalue computation

2020 ◽  
Vol 42 (10) ◽  
pp. 1908-1920
Author(s):  
Ping Yang ◽  
Yao-Lin Jiang
Keyword(s):  
Model Reduction ◽  
Newton Method ◽  
Reduction Method ◽  
Linear Time ◽  
Singular Values ◽  
Linear Time Invariant ◽  
Hankel Singular Values ◽  
Davidson Method ◽  
Reduction Methods ◽  
Linear Time Invariant Systems

This paper provides three model reduction methods for linear time-invariant systems in the view of the Riemannian Newton method and the Jacobi-Davidson method. First, the computation of Hankel singular values is converted into the linear eigenproblem by the similarity transformation. The Riemannian Newton method is used to establish the model reduction method. Besides, we introduce the Jacobi-Davidson method with the block version for the linear eigenproblem and present the corresponding model reduction method, which can be seen as an acceleration of the former method. Both the resulting reduced systems can be equivalent to the reduced system originating from a balancing transformation. Then, the computation of Hankel singular values is transformed into the generalized eigenproblem. The Jacobi-Davidson method is employed to establish the model reduction method, which can also lead to the reduced system equivalent to that resulting from a balancing transformation. This method can also be regarded as an acceleration of a Riemannian Newton method. Moreover, the application for model reduction of nonlinear systems with inhomogeneous conditions is also investigated.

scholarly journals Stability Analysis of Linear Feedback Systems in Control

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1518
Author(s):  
Mutti-Ur Rehman ◽  
Jehad Alzabut ◽  
Muhammad Fazeel Anwar
Keyword(s):  
System Theory ◽  
Stability Analysis ◽  
Linear Time ◽  
Singular Values ◽  
Low Rank ◽  
Gradient System ◽  
Feedback Systems ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

This article presents a stability analysis of linear time invariant systems arising in system theory. The computation of upper bounds of structured singular values confer the stability analysis, robustness and performance of feedback systems in system theory. The computation of the bounds of structured singular values of Toeplitz and symmetric Toeplitz matrices for linear time invariant systems is presented by means of low rank ordinary differential equations (ODE’s) based methodology. The proposed methodology is based upon the inner-outer algorithm. The inner algorithm constructs and solves a gradient system of ODE’s while the outer algorithm adjusts the perturbation level with fast Newton’s iteration. The comparison of bounds of structured singular values approximated by low rank ODE’s based methodology results tighter bounds when compared with well-known MATLAB routine mussv, available in MATLAB control toolbox.

Model Reduction of Large-Scale Discrete Plants With Specified Frequency Domain Balanced Structure

2004 ◽  
Vol 127 (3) ◽  
pp. 486-498 ◽  
Author(s):  
Abbas H. Zadegan ◽  
Ali Zilouchian
Keyword(s):  
Model Reduction ◽  
Frequency Domain ◽  
Large Scale ◽  
Linear Time ◽  
Model Simulation ◽  
Large Scale Systems ◽  
Linear Time Invariant ◽  
Balanced Structure ◽  
Linear Time Invariant Systems ◽  
Model Reduction Technique

A new model reduction technique for linear time-invariant systems is proposed. A new method that reduces the order of large-scale systems by integrating singular perturbation with specified frequency domain balanced structure is proposed. Considering a frequency range at which the system actually operates guarantees a good approximation of the original full order model. Simulation experiments for model reduction of several large-scale systems demonstrate the effectiveness of the proposed technique.

scholarly journals Frequency Weighted Controller Order Reduction (Part I)

2010 ◽  
Vol 61 (3) ◽  
pp. 141-148 ◽  
Author(s):  
Roozbeh Sadeghian ◽  
Paknosh Karimaghaee ◽  
Alireza Khayatian
Keyword(s):  
Model Reduction ◽  
Linear Time ◽  
Main Idea ◽  
Order Reduction ◽  
New Method ◽  
Frequency Model ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Output Characteristics ◽  
The Stability

Frequency Weighted Controller Order Reduction (Part I) In this paper, a new method for controller reduction of linear time invariant systems is presented. The method is based on newly defined controllability and observability grammians which are calculated from input to state and state to output characteristics of the controller in a certain frequency domain. These grammians are defined for the closed loop system to keep the performance of original controller. The main idea of this method is based on Moores model reduction. The relation of this method with weighted frequency model reduction of Enns will be described by a commutative diagram. The stability property of the new method is investigated. It is shown that the stability for two sided weights can be preserved under certain conditions. The simulation results show the effectiveness of this novel technique.

scholarly journals Stability preserving model reduction for linearly coupled linear time-invariant systems

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 817-818
Author(s):  
Peter Benner ◽  
Sara Grundel ◽  
Petar Mlinarić
Keyword(s):  
Model Reduction ◽  
Linear Time ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

scholarly journals Lanczos Model Reduction for Switched Linear Systems

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Model Reduction ◽  
Large Scale ◽  
Krylov Subspace ◽  
Linear Time ◽  
Lanczos Algorithm ◽  
Linear Time Invariant ◽  
New Methods ◽  
Reduction Methods ◽  
Non Linear System ◽  
Time Invariant

In today the methods reduction of large-scale linear time invariant and complexe systems are very many, the best choices today is the used of the krylov subspace methods based on moment matching. As hybrid dynamical systems are of rising spread and complexity, for these reasons, we present in this paper two model reduction methods applied to linear switched system. Which is an important class of hybrid and non linear system. Tow methods for reduction systems are present. In first part we present the modified non symmetric Lanczos algorithm, which is numerically efficient and applicable of any order. In second part we present the modified global lanczos algorithm, it is also numerically efficient, applicable of any order and having a best numerical stability. The effectivity and suitability of these new methods is illustrated by one simulation example.

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