Design of linear feedback for bilinear control systems

Vasiliy Belozyorov

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 4, page 493-511
  • ISSN: 1641-876X

Abstract

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Sufficient conditions for the conditional stability of trivial solutions for quadratic systems of ordinary differential equations are obtained. These conditions are then used to design linear control laws on the output for a bilinear system of any order. In the case of a homogeneous system, a domain of the conditional stability is also indicated (it is a cone). Some examples are given.

How to cite

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Belozyorov, Vasiliy. "Design of linear feedback for bilinear control systems." International Journal of Applied Mathematics and Computer Science 12.4 (2002): 493-511. <http://eudml.org/doc/207605>.

@article{Belozyorov2002,
abstract = {Sufficient conditions for the conditional stability of trivial solutions for quadratic systems of ordinary differential equations are obtained. These conditions are then used to design linear control laws on the output for a bilinear system of any order. In the case of a homogeneous system, a domain of the conditional stability is also indicated (it is a cone). Some examples are given.},
author = {Belozyorov, Vasiliy},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {cone of stability; bilinear control system; linear control law; closed-loop system; feedback; system of ordinary quadratic differential equations},
language = {eng},
number = {4},
pages = {493-511},
title = {Design of linear feedback for bilinear control systems},
url = {http://eudml.org/doc/207605},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Belozyorov, Vasiliy
TI - Design of linear feedback for bilinear control systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 4
SP - 493
EP - 511
AB - Sufficient conditions for the conditional stability of trivial solutions for quadratic systems of ordinary differential equations are obtained. These conditions are then used to design linear control laws on the output for a bilinear system of any order. In the case of a homogeneous system, a domain of the conditional stability is also indicated (it is a cone). Some examples are given.
LA - eng
KW - cone of stability; bilinear control system; linear control law; closed-loop system; feedback; system of ordinary quadratic differential equations
UR - http://eudml.org/doc/207605
ER -

References

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  1. Belozyorov V.Ye. (2001): On an invariant design of feedback for bilinear control systems of second order. - Int. J. Appl. Math.Comp. Sci., Vol. 11, No. 2, pp. 377-389. Zbl1073.93526
  2. Bowen J.H. and Masters E.F.O. (1959): Nuclear Reactor Control and Instrumentation. - London: Temple Press Limited. 
  3. Demidovich B.P. (1967): Lectures on the Mathematical Theory of Stability. - Moscow: Nauka, (in Russian). Zbl0155.41601
  4. Demidovich B.P. and Maron I.A. (1966): Fundamentals of Computational Mathematics. - Moscow: Nauka, (in Russian). 
  5. Gantmacher F.R. (1990): Theory of Matrices. -Chelsea: Chelsea Pub Co. Zbl0085.01001
  6. Fulton W. (1984): Intersection Theory. - Berlin: Springer. Zbl0541.14005
  7. Khalil H. (1995): Nonlinear Systems, 2nd Ed. - New-York: Prentice Hall. 

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