| Title:
|
Characterization of generic properties of linear structured systems for efficient computations (English) |
| Author:
|
Commault, Christian |
| Author:
|
Dion, Jean-Michel |
| Author:
|
van der Woude, Jacob W. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
38 |
| Issue:
|
5 |
| Year:
|
2002 |
| Pages:
|
[503]-520 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate some of the computational aspects of generic properties of linear structured systems. In such systems only the zero/nonzero pattern of the system matrices is assumed to be known. For structured systems a number of characterizations of so-called generic properties have been obtained in the literature. The characterizations often have been presented by means of the graph associated to a linear structured system and are then expressed in terms of the maximal or minimal number of certain type of vertices contained in a combination of specific paths. In this paper we give new graph theoretic characterizations of structural invariants of structured systems. It turns out that these new characterizations allow to compute these invariants via standard and efficient algorithms from combinatorial optimization. (English) |
| Keyword:
|
linear structured system |
| Keyword:
|
graph theoretic characterizations of structural invariants |
| MSC:
|
93B10 |
| MSC:
|
93B40 |
| MSC:
|
93C05 |
| MSC:
|
94C15 |
| idZBL:
|
Zbl 1265.93120 |
| idMR:
|
MR1966942 |
| . |
| Date available:
|
2009-09-24T19:48:20Z |
| Last updated:
|
2015-03-25 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135483 |
| . |
| Reference:
|
[1] Commault C., Dion J. M., Perez A.: Disturbance rejection for structured systems.IEEE Trans. Automat. Control AC-36 (1991), 884–887 Zbl 0754.93023, MR 1109830, 10.1109/9.85072 |
| Reference:
|
[2] Descusse J., Dion J. M.: On the structure at infinity of linear square decouplable systems.IEEE Trans. Automat. Control AC-27 (1982), 971–974 MR 0680500, 10.1109/TAC.1982.1103041 |
| Reference:
|
[3] Dion J. M., Commault C.: Smith–McMillan factorisations at infinity of rational matrix functions and their control interpretation.Systems Control Lett. 1 (1982), 312–320 MR 0670218, 10.1016/S0167-6911(82)80029-7 |
| Reference:
|
[4] Dion J. M., Commault C.: Feedback decoupling of structured systems.IEEE Trans. Automat. Control AC-38 (1993), 1132–1135 Zbl 0800.93470, MR 1235238, 10.1109/9.231471 |
| Reference:
|
[5] Dion J. M., Commault, C., Montoya J.: Simultaneous decoupling and disturbance rejection – a structural approach.Internat. J. Control 59 (1994), 1325–1344 Zbl 0800.93477, MR 1277265, 10.1080/00207179408923133 |
| Reference:
|
[6] Glover K., Silverman L. M.: Characterization of structural controllability.IEEE Trans. Automat. Control AC-21 (1976), 534–537 Zbl 0332.93012, MR 0424299, 10.1109/TAC.1976.1101257 |
| Reference:
|
[7] Gondran M., Minoux M.: Graphs and Algorithms.Wiley, New York 1984 Zbl 1172.05001, MR 0745802 |
| Reference:
|
[8] Hopcroft J. E., Karp R. M.: An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.SIAM J. Comput. 2 (1973), 225–231 MR 0337699, 10.1137/0202019 |
| Reference:
|
[9] Hosoe S.: Determination of generic dimensions of controllable subspaces and applications.IEEE Trans. Automat. Control AC-25 (1980), 1192–1196 MR 0601504, 10.1109/TAC.1980.1102506 |
| Reference:
|
[10] Hovelaque V.: Analyse Structurelle, Géométrique, et Graphique des Systèmes Linéaires Structurés, Thèse de Doctorat.Inst. Nat. Polytechnique de Grenoble 1997 |
| Reference:
|
[11] Hovelaque V., Commault, C., Dion J. M.: Analysis of linear structured systems using a primal-dual algorithm.Systems Control Lett. 27 (1996), 73–85 Zbl 0875.93117, MR 1388501, 10.1016/0167-6911(95)00039-9 |
| Reference:
|
[12] Hovelaque V., Commault, C., Dion J. M.: Disturbance decoupling for linear structured systems via a primal-dual algorithm.Comp. Engrg. Syst. Appl. IMACS Lille (1996), 455–459 |
| Reference:
|
[13] Hovelaque V., Djidi N., Commault, C., Dion J. M.: Decoupling problem for structured systems via a primal-dual algorithm.In: Proc. European Control Conference (ECC97), Brussels 1997 |
| Reference:
|
[14] Kuhn H. W.: The Hungarian method for the assignment problem.Nav. Res. Log. Quat. 2 (1955), 83–97 Zbl 0143.41905, MR 0075510, 10.1002/nav.3800020109 |
| Reference:
|
[15] Lin C. T.: Structural controllability.IEEE Trans. Automat. Control AC-19 (1974), 201–208 Zbl 0343.93009, MR 0452870, 10.1109/TAC.1974.1100557 |
| Reference:
|
[16] Linnemann A.: Decoupling of structured systems.Systems Control Lett. 1 (1981), 79–86 Zbl 0475.93049, MR 0670045, 10.1016/S0167-6911(81)80040-0 |
| Reference:
|
[17] Murota K.: System analysis by graphs and matroids, Algorithms and Combinatorics.Springer–Verlag, New York 1987 MR 0897529 |
| Reference:
|
[18] Reinschke K. J.: Multivariable Control: A Graph–heoretic Approach.Springer–Verlag, New York 1988 MR 0962644 |
| Reference:
|
[19] Röbenack K., Reinschke K. J.: Digraph based determination of Jordan block size structure of singular matrix pencils.Linear Algebra Appl. 275–276 (1998), 495–507 Zbl 0934.15012, MR 1628406 |
| Reference:
|
[20] Schizas C., Evans F. J.: A graph theoretic approach to multivariable control system design.Automatica 17 (1981), 371–377 Zbl 0476.93041, 10.1016/0005-1098(81)90054-6 |
| Reference:
|
[21] Shields R. W., Pearson J. B.: Structural controllability of multi-input linear systems.IEEE Trans. Automat. Control AC-21 (1976), 203–212 MR 0462690, 10.1109/TAC.1976.1101198 |
| Reference:
|
[22] Söte W.: Eine graphische Methode zur Ermittlung der Nullstellen in Mehrgrössensystemen.Reglungstechnik 28 (1980), 346–348 Zbl 0459.93027 |
| Reference:
|
[23] Suda N., Wan, B., Ueno I.: The orders of infinite zeros of structured systems.Trans. Soc. Instr. Control Engineers 25 (1989), 346–348 |
| Reference:
|
[24] Woude J. W. van der: On the structure at infinity of a structured system.Linear Algebra Appl. 148 (1991), 145–169 MR 1090758 |
| Reference:
|
[25] Woude J. W. van der: The generic number of invariant zeros of a structured linear system.SIAM J. Control Optim. 38 (2000), 1, 1–21 MR 1740610, 10.1137/S0363012996310119 |
| Reference:
|
[26] Woude J. W. van der: The generic canonical form of a regular structured matrix pencil.Linear Algebra Appl. 353 (2002), 267–288 MR 1919642 |
| Reference:
|
[27] Woude J. W. van der, Commault, C., Dion J. M.: Invariants for linear structured systems.Internal report of the Laboratoire d’Automatique de Grenoble 2000 |
| Reference:
|
[28] Yamada T.: A network flow algorithm to find an elementary I/O matching.Networks 18 (1988), 105–109 Zbl 0641.90039, MR 0939147, 10.1002/net.3230180203 |
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