Conditions on Decomposing Linear Systems With More Than One Matrix to Block Triangular or Diagonal Form

This technical note provides necessary and sufficient conditions to determine that a linear system with more than one matrix in its state-space representation can be decomposed into cascade or separate sub-systems. In order to perform such decomposition, one needs to determine a linear transformatio...

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Published in:IEEE transactions on automatic control 2015-01, Vol.60 (1), p.233-239
Main Authors: Mesbahi, Afshin, Haeri, Mohammad
Format: Article
Language:English
Subjects:
Automatic control
Blocking
Decomposition
Eigenvalues and eigenfunctions
Equations
Linear systems
Linear transformations
Mathematical models
Matrices
Representations
Scalars
Stability analysis
Sufficient conditions
Transforms
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description This technical note provides necessary and sufficient conditions to determine that a linear system with more than one matrix in its state-space representation can be decomposed into cascade or separate sub-systems. In order to perform such decomposition, one needs to determine a linear transformation matrix. Furthermore, the given conditions are adapted to a simple but effective condition to derive all possible scalar sub-systems for a given linear system. Numerical examples are provided to demonstrate the applicability of the presented results.
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subjects Automatic control
Blocking
Decomposition
Eigenvalues and eigenfunctions
Equations
Linear systems
Linear transformations
Mathematical models
Matrices
Representations
Scalars
Stability analysis
Sufficient conditions
Transforms
title Conditions on Decomposing Linear Systems With More Than One Matrix to Block Triangular or Diagonal Form
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