On an invariant design of feedbacks for bilinear control systems of second order

Vasiliy Belozyorov

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 2, page 377-389
  • ISSN: 1641-876X

Abstract

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The problem of linear feedback design for bilinear control systems guaranteeing their conditional closed-loop stability is considered. It is shown that this problem can be reduced to investigating the conditional stability of solutions of quadratic systems of differential equations depending on parameters of the control law. Sufficient conditions for stability in the cone of a homogeneous quadratic system are obtained. For second-order systems, invariant conditions of conditional asymptotic stability are found.

How to cite

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Belozyorov, Vasiliy. "On an invariant design of feedbacks for bilinear control systems of second order." International Journal of Applied Mathematics and Computer Science 11.2 (2001): 377-389. <http://eudml.org/doc/207512>.

@article{Belozyorov2001,
abstract = {The problem of linear feedback design for bilinear control systems guaranteeing their conditional closed-loop stability is considered. It is shown that this problem can be reduced to investigating the conditional stability of solutions of quadratic systems of differential equations depending on parameters of the control law. Sufficient conditions for stability in the cone of a homogeneous quadratic system are obtained. For second-order systems, invariant conditions of conditional asymptotic stability are found.},
author = {Belozyorov, Vasiliy},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {second order systems; asymptoticstability; bilinear control systems; invariant design},
language = {eng},
number = {2},
pages = {377-389},
title = {On an invariant design of feedbacks for bilinear control systems of second order},
url = {http://eudml.org/doc/207512},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Belozyorov, Vasiliy
TI - On an invariant design of feedbacks for bilinear control systems of second order
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 2
SP - 377
EP - 389
AB - The problem of linear feedback design for bilinear control systems guaranteeing their conditional closed-loop stability is considered. It is shown that this problem can be reduced to investigating the conditional stability of solutions of quadratic systems of differential equations depending on parameters of the control law. Sufficient conditions for stability in the cone of a homogeneous quadratic system are obtained. For second-order systems, invariant conditions of conditional asymptotic stability are found.
LA - eng
KW - second order systems; asymptoticstability; bilinear control systems; invariant design
UR - http://eudml.org/doc/207512
ER -

References

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  1. Bellman R. (1976): Introduction to the Theory of Matrices. -Moscow: Nauka, (in Russian). 
  2. Belozyorov V.Ye. and Poddubnaya O.A. (2000): Algebraici analysis of a conditional stability of solutions of quadratic systems of the differential equations. - Problems of Control and Computer Science, No.2, pp.13-23, (inRussian). 
  3. Borisenko S.D. and Kosolapov V.I. et al. (1988): A Stability of Processes for Continuous and Discrete Perturbations. -Kiev: Naukova Dumka, (in Russian). Zbl0708.34045
  4. Demidovich B.P. (1967): Lectures on the Mathematical Theory of Stability. - Moscow: Nauka, (in Russian). Zbl0155.41601
  5. Gantmacher F.R. (1990): The Theory of Matrices. - Chelsea: Chelsea PubCo. Zbl0085.01001
  6. Isidori A. (1995): Nonlinear Control Systems, 3rd Ed. - London: Springer. Zbl0878.93001
  7. Khalil H. (1995): Nonlinear Systems, 2nd Ed. -New York: Prentice Hall. 
  8. Sibirsky K.S. (1982): Introduction to the Algebraic Theory of Invariants of Differential Equations. - Kishinev: Shtinica, (in Russian). 
  9. Zubov V.I. (1974): Mathematical Methods of Studying Systems of Automatic Control. - Leningrad: Mashinostroyeniye, (in Russian). 

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