Differential geometric structures of stable state feedback systems with dual connections

Atsumi Ohara; Shun-ichi Amari

Kybernetika (1994)

  • Volume: 30, Issue: 4, page 369-386
  • ISSN: 0023-5954

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Ohara, Atsumi, and Amari, Shun-ichi. "Differential geometric structures of stable state feedback systems with dual connections." Kybernetika 30.4 (1994): 369-386. <http://eudml.org/doc/27314>.

@article{Ohara1994,
author = {Ohara, Atsumi, Amari, Shun-ichi},
journal = {Kybernetika},
keywords = {stabilizing feedbacks; linear; fiber metric; dual connections; flatness},
language = {eng},
number = {4},
pages = {369-386},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Differential geometric structures of stable state feedback systems with dual connections},
url = {http://eudml.org/doc/27314},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Ohara, Atsumi
AU - Amari, Shun-ichi
TI - Differential geometric structures of stable state feedback systems with dual connections
JO - Kybernetika
PY - 1994
PB - Institute of Information Theory and Automation AS CR
VL - 30
IS - 4
SP - 369
EP - 386
LA - eng
KW - stabilizing feedbacks; linear; fiber metric; dual connections; flatness
UR - http://eudml.org/doc/27314
ER -

References

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  2. S. Amari, Differential geometry of a parametric family of invertible linear systems -- Riemannian metric, dual affine connections, and divergence, Math. Systems Theory 20 (1987), 53-83. (1987) Zbl0632.93017MR0901894
  3. P. S. Krishnaprasad, Symplectic mechanics and rational functions, Ricerche Automat. 10 (1979), 2, 107-135. (1979) MR0614258
  4. A. D. C. Youla H. A. Jabr, J. J. Bongiorno, Modern Wiener-Hopf design of optimal controllers. Part II -- the multivariable case, IEEE Trans. Automat. Control 21 (1976), 319-338. (1976) MR0446637
  5. V. Kučera, Discrete Linear Control: The Polynomial Equation Approach, Wiley, Chichester 1979. (1979) MR0573447
  6. A. Ohara, T. Kitamori, Geometric structures of stable state feedback systems, In: Proc. of 29th IEEE C.D.C. 1990, pp. 2494-2490, and IEEE Trans. Automat. Control 38 (1993), 10, 1579-1583. (1990) MR1242914
  7. A. Ohara, S. Amari, Differential geometric structures of stable state feedback systems with dual connections, In: Proc. 2nd IFAC Workshop on System Structure and Control 1992, pp. 176-179. (1992) 
  8. S. Amari, Differential-Geometrical Methods in Statistics, Springer-Verlag, Berlin 1985. (1985) Zbl0559.62001MR0788689
  9. A. Ohara S. Nakazumi, N. Suda, Relations between a parametrization of stabilizing state feedback gains and eigenvalue locations, Systems Control Lett. 16 (1991), 261-266. (1991) MR1102211
  10. S. Kobayashi, K. Nomizu, Foundations of Differential Geometry II, J. Wiley, New York 1969. (1969) 
  11. S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York 1962. (1962) Zbl0111.18101MR0145455
  12. M. Takeuchi, Lie Groups II, Iwanami, Tokyo 1978 (in Japanese). (1978) MR0839859

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