# 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

## Access Full Article

top## Abstract

top## How to cite

topAugusto 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

top- [1] A. Ben-Israel and Th. N. E. Greville, Generalized Inverses, Theory and Applications, 2nd edition, Springer, New York, 2003. Zbl1026.15004
- [2] F. Cecioni, Sopra operazioni algebriche, Ann. Scuola Nom. Sup. Pisa Sci. Fis. Mat. 11 (1910), 17–20.
- [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] B. De Schutter, Minimal state-space realization in linear system theory: An overview, J. Comput. Appl. Math. 121 (2000) , 331–354. Zbl0963.93008
- [5] A. Ferrante and H. K. Wimmer, Reachability matrices and cyclic matrices, Electron. J. Linear Algebra 20 (2010), 95–102. Zbl1198.15009
- [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] S. J. Qin, An overview of subspace identification, Comput. Chem. Eng. 30 (2006), 1502–1513. [Crossref]
- [8] C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and Its Applications, Wiley, New York, 1971. Zbl0236.15004
- [9] E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, 2nd edition., Springer, New York, 1998. Zbl0945.93001
- [10] A. J. Tether, Construction of minimal linear state-variable models from finite input-output data, IEEE Trans. Automat. Control. 15 (1970), 427–436.