Geodesic
External properness
Kybernetika, Tome 44 (2008) no. 3, pp. 360-372 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper, we revisit the structural concept of properness. We distinguish between the properness of the whole system, here called internal properness, and the properness of the “observable part” of the system. We give geometric characterizations for this last properness concept, namely external properness.
In this paper, we revisit the structural concept of properness. We distinguish between the properness of the whole system, here called internal properness, and the properness of the “observable part” of the system. We give geometric characterizations for this last properness concept, namely external properness.
Classification : 93B27, 93C05, 93C35
Keywords: properness; linear systems; implicit systems 
@article{KYB_2008_44_3_a6,
     author = {Bonilla, Mois\'es and Malabre, Michel and Pacheco, Jaime},
     title = {External properness},
     journal = {Kybernetika},
     pages = {360--372},
     year = {2008},
     volume = {44},
     number = {3},
     mrnumber = {2436037},
     zbl = {1154.93329},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2008_44_3_a6/}
}
TY  - JOUR
AU  - Bonilla, Moisés
AU  - Malabre, Michel
AU  - Pacheco, Jaime
TI  - External properness
JO  - Kybernetika
PY  - 2008
SP  - 360
EP  - 372
VL  - 44
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_2008_44_3_a6/
LA  - en
ID  - KYB_2008_44_3_a6
ER  - 
%0 Journal Article
%A Bonilla, Moisés
%A Malabre, Michel
%A Pacheco, Jaime
%T External properness
%J Kybernetika
%D 2008
%P 360-372
%V 44
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_2008_44_3_a6/
%G en
%F KYB_2008_44_3_a6
Bonilla, Moisés; Malabre, Michel; Pacheco, Jaime. External properness. Kybernetika, Tome 44 (2008) no. 3, pp. 360-372. http://geodesic.mathdoc.fr/item/KYB_2008_44_3_a6/

[1] Aplevich J. D.: Time-domain input-output Representations of linear systems. Automatica 17 (1981), 3, 509–522 | MR | Zbl

[2] Aplevich J. D.: Implicit Linear Systems. (Lecture Notes in Control and Information Sciences 152.) Springer–Verlag, Berlin 1991 | MR | Zbl

[3] Armentano V. A.: The pencil $\left( sE-A\right)$ and controllability-observability for generalized linear systems: a geometric approach. SIAM J. Control Optim. 24 (1986), 4, 616–638 | MR

[4] Bernhard P.: On singular implicit dynamical systems. SIAM J. Control Optim. 20 (1982), 5, 612–633 | MR

[5] Bonilla M., Malabre M.: Geometric minimization under external equivalence for implicit descriptions. Automatica 31 (1995), 6, 897–901 | MR | Zbl

[6] Bonilla M., Malabre M.: Structural matrix minimization algorithm for implicit descriptions. Automatica 33 (1997), 4, 705–710 | MR | Zbl

[7] Bonilla M., Malabre, M., Fonseca M.: On the approximation of non–proper control laws. Internat. J. Control 68 (1997), 4, 775–796 | MR | Zbl

[8] Bonilla M., Malabre M.: More about non square implicit descriptions for modelling and control. In: Proc. 39th IEEE Conference on Decision and Control 2000, pp. 3642–3647

[9] Bonilla M., Malabre M.: On the control of linear systems having internal variations. Automatica 39 (2003), 11, 1989–1996 | MR

[10] Campbell S. L.: Singular Systems of Differential Equations II. Pitman, New York 1982 | MR | Zbl

[11] Cobb D.: Controllability, Observability and Duality in Singular Systems. IEEE Trans. Automat. Control AC-29 (1984), 12, 1076–1082 | MR

[12] Dai L.: Singular Control Systems. (Lecture Notes in Control and Information Sciences 118.) Springer–Verlag, Berlin 1989 | MR | Zbl

[13] Frankowska H.: On the controllability and observability of implicit systems. Systems Control Lett. 14 (1990), 219–225 | MR

[14] Gantmacher F. R.: The Theory of Matrices. Vol. II. Chelsea, New York 1977 | Zbl

[15] Kučera V., Zagalak P.: Fundamental theorem of state feedback for singular systems. Automatica 24 (1988), 5, 653–658 | MR

[16] Kuijper M.: First-order Representations of Linear Systems. Ph.D. Thesis. Katholieke Universiteit Brabant, Amsterdam 1992 | Zbl

[17] Kuijper M.: Descriptor representations without direct feedthrough term. Automatica 28 (1992), 633–637 | MR | Zbl

[18] Lewis F. L.: A survey of linear singular systems. Circuits Systems Signal Process. 5 (1986), 1, 3–36 | MR | Zbl

[19] Lewis F. L.: A tutorial on the geometric analysis of linear time-invariant implicit systems. Automatica 28 (1992), 1, 119–137 | MR | Zbl

[20] Loiseau J. J.: Some geometric considerations about the Kronecker normal form. Internat. J. Control 42 (1985), 6, 1411–1431 | MR | Zbl

[21] Malabre M.: Generalized linear systems, geometric and structural approaches. Linear Algebra Appl. 122/123/124 (1989), 591–621 | MR | Zbl

[22] Malabre M.: More geometry about singular systems. In: Proc. 26th IEEE Conference on Decision and Control 1987, pp. 1138–1139

[23] Özçaldiran K.: A geometric characterization of the reachable and controllable subspaces of descriptor systems. Circuits Systems Signal Process. 5 (1986), 1, 37–48 | MR

[24] Pacheco P., Bonilla, M., Malabre M.: Proper exponential approximation of non proper compensators: The MIMO case. In: Proc. 42nd IEEE Conference on Decision and Control 2003, pp. 110–115

[25] Polderman J. W., Willems J. C.: Introduction to Mathematical Systems Theory: A Behavioral Approach. Springer–Verlag, New York 1998 | MR | Zbl

[26] Rosenbrock H. H.: State-Space and Multivariable Theory. Nelson, London 1970 | MR | Zbl

[27] Schwartz L.: Théorie des Distributions. Herman, Paris 1966 | MR | Zbl

[28] Verghese G. C.: Further notes on singular descriptions. JACC TA4 (1981), Charlottesville

[29] Verghese G. C., Lévy B. C., Kailath T.: A generalized state-space for singular systems. IEEE Trans. Automat. Control 26 (1981), 4, 811–831 | MR

[30] Willems J. C.: Input-output and state space representations of finite-dimensional linear time-invariant systems. Linear Algebra Appl. 50 (1983), 81–608 | MR | Zbl

[31] Wong K. T.: The eigenvalue problem $\lambda Tx+Sx. $ J. Differential Equations 1 (1974), 270–281 | MR | Zbl

[32] Zagalak P., Kučera V.: Fundamental theorem of state feedback: The case of infinite poles. Kybernetika 27 (1991), 1, 1–11 | MR | Zbl