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Conditions on decomposing linear systems with more than one matrix to block triangular or diagonal form

Mesbahi, A ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.1109/TAC.2014.2326292
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2015
  4. Abstract:
  5. 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
  6. Keywords:
  7. Simultaneous block triangularization stability ; Decomposition ; Linear systems ; Mathematical transformations ; Matrix algebra ; State space methods ; Block diagonalization ; Block triangularization ; Linear transformation matrix ; Similarity transformation ; Simultaneous ; State space representation ; Sub-systems ; Technical notes ; Linear transformations
  8. Source: IEEE Transactions on Automatic Control ; Volume 60, Issue 1 , May , 2015 , Pages 233-239 ; 00189286 (ISSN)
  9. URL: http://ieeexplore.ieee.org/document/6819395