Pairs of k -step reachability and m -step observability matrices

Augusto Ferrante; Harald K. Wimmer

Special Matrices (2013)

  • Volume: 1, page 25-27
  • ISSN: 2300-7451

Abstract

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Let V and W be matrices of size n × pk and qm × n, respectively. A necessary and sufficient condition is given for the existence of a triple (A,B,C) such that V a k-step reachability matrix of (A,B) andW an m-step observability matrix of (A,C).

How to cite

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Augusto Ferrante, and Harald K. Wimmer. " Pairs of k -step reachability and m -step observability matrices ." Special Matrices 1 (2013): 25-27. <http://eudml.org/doc/267506>.

@article{AugustoFerrante2013,
abstract = {Let V and W be matrices of size n × pk and qm × n, respectively. A necessary and sufficient condition is given for the existence of a triple (A,B,C) such that V a k-step reachability matrix of (A,B) andW an m-step observability matrix of (A,C).},
author = {Augusto Ferrante, Harald K. Wimmer},
journal = {Special Matrices},
keywords = {Reachability matrix; observability matrix; generalized inverses; common solutions; reachability matrix},
language = {eng},
pages = {25-27},
title = { Pairs of k -step reachability and m -step observability matrices },
url = {http://eudml.org/doc/267506},
volume = {1},
year = {2013},
}

TY - JOUR
AU - Augusto Ferrante
AU - Harald K. Wimmer
TI - Pairs of k -step reachability and m -step observability matrices
JO - Special Matrices
PY - 2013
VL - 1
SP - 25
EP - 27
AB - Let V and W be matrices of size n × pk and qm × n, respectively. A necessary and sufficient condition is given for the existence of a triple (A,B,C) such that V a k-step reachability matrix of (A,B) andW an m-step observability matrix of (A,C).
LA - eng
KW - Reachability matrix; observability matrix; generalized inverses; common solutions; reachability matrix
UR - http://eudml.org/doc/267506
ER -

References

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  2. [2] F. Cecioni, Sopra operazioni algebriche, Ann. Scuola Nom. Sup. Pisa Sci. Fis. Mat. 11 (1910), 17–20. 
  3. [3] M. Dahleh, M. A. Dahleh, and G. Verghese, Lectures on Dynamic Systems and Control, MIT Lectures, 2004. Available online: web.mit.edu/6.241/www/chapter_22.pdf web.mit.edu/6.241/www/chapter_26.pdf 
  4. [4] B. De Schutter, Minimal state-space realization in linear system theory: An overview, J. Comput. Appl. Math. 121 (2000) , 331–354. Zbl0963.93008
  5. [5] A. Ferrante and H. K. Wimmer, Reachability matrices and cyclic matrices, Electron. J. Linear Algebra 20 (2010), 95–102. Zbl1198.15009
  6. [6] E. W. Kamen, P. P. Khargonekar, and K. R. Poolla, A transfer function approach to linear time-varying discrete-time systems, SIAM J. Control Optim. 23 (1985), 550–565. [Crossref] Zbl0626.93039
  7. [7] S. J. Qin, An overview of subspace identification, Comput. Chem. Eng. 30 (2006), 1502–1513. [Crossref] 
  8. [8] C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and Its Applications, Wiley, New York, 1971. Zbl0236.15004
  9. [9] E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, 2nd edition., Springer, New York, 1998. Zbl0945.93001
  10. [10] A. J. Tether, Construction of minimal linear state-variable models from finite input-output data, IEEE Trans. Automat. Control. 15 (1970), 427–436. 

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