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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Bibliographic Details
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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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2014.2326292