On generic properties of linear systems: An overview

Krzysztof Tchoń

Kybernetika (1983)

  • Volume: 19, Issue: 6, page 467-474
  • ISSN: 0023-5954

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Tchoń, Krzysztof. "On generic properties of linear systems: An overview." Kybernetika 19.6 (1983): 467-474. <http://eudml.org/doc/27859>.

@article{Tchoń1983,
author = {Tchoń, Krzysztof},
journal = {Kybernetika},
keywords = {invertibility; structural stability; generic controllability},
language = {eng},
number = {6},
pages = {467-474},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On generic properties of linear systems: An overview},
url = {http://eudml.org/doc/27859},
volume = {19},
year = {1983},
}

TY - JOUR
AU - Tchoń, Krzysztof
TI - On generic properties of linear systems: An overview
JO - Kybernetika
PY - 1983
PB - Institute of Information Theory and Automation AS CR
VL - 19
IS - 6
SP - 467
EP - 474
LA - eng
KW - invertibility; structural stability; generic controllability
UR - http://eudml.org/doc/27859
ER -

References

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  2. R. W. Brockett, M. D. Mesarović, The reproducibility of multivariable systems, J. Math. Anal. Appl. 11 (1965), 548-563. (1965) MR0184743
  3. P. Brunovský, A classification of linear controllable systems, Kybernetika 6 (1970), 3, 173-187. (1970) MR0284247
  4. L. E. Dickson, Theory of Numbers, Vol. II. Chelsea, New York 1971. (1971) 
  5. G. H. Hardy, S. Ramanujan, Asymptotic formulae in combinatory analysis, Proc. London Math. Soc. 17 (1918), 75-115. (1918) MR1575586
  6. R. Hermann, C. Martin, Algebro-Geometric and Lie-Theoretic Techniques in Systems Theory. Part A, Math. Sci. Press, Brookline 1977. (1977) Zbl0362.93002MR0490123
  7. R. E. Kalman, Algebraic geometric description of the class of linear systems of constant dimension, Proc. 8th Annual Princeton Conf. on Inform. Sci. and Systems, Princeton 1974. (1974) 
  8. A. W. Olbrot, Genericity and non-genericity of properties of mathematical models, Arch. Automat. Telemech. 5 (1980), 4, 473-481 (in Polish). (1980) MR0626086
  9. J. Palis, Jr., W. de Melo, Geometric Theory of Dynamical Systems, Springer-Verlag, Berlin 1982. (1982) Zbl0491.58001MR0669541
  10. M. K. Sain, J. L. Massey, Invertibility of linear time-invariant systems, IEEE Trans. Automat. Control AC-15 (1969), 141-149. (1969) MR0246664
  11. K. Tchoń, On some operations preserving generic properties of systems, Internat. J. Gen. Systems 9 (1983), 89-94. (1983) MR0705713
  12. R. Thom, Structural Stability and Morphogenesis, Benjamin, New York 1975. (1975) Zbl0303.92002MR0488156
  13. F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Scott-Foresman, Glenview 1971. (1971) Zbl0241.58001MR0295244
  14. J. C. Willems, Topological classification and structural stability of linear systems, J. Differential Equations 35 (1980), 306 - 318. (1980) Zbl0394.93024MR0563384
  15. J. C. Willems, W. H. Hesselink, Generic properties of the pole placement problem, Proc. 1978 IFAC Congress, Helsinki, Finland, 1725-1729. (1978) 
  16. W. M. Wonham, Linear Multivariable Control: A Geometric Approach, Second Edition. Springer-Verlag, Berlin 1979. (1979) Zbl0424.93001MR0569358

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