A constructive method for solving stabilization problems
Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2000)
- Volume: 20, Issue: 1, page 51-62
- ISSN: 1509-9407
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Abstract
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topVadim Azhmyakov. "A constructive method for solving stabilization problems." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 20.1 (2000): 51-62. <http://eudml.org/doc/271557>.
@article{VadimAzhmyakov2000,
abstract = {The problem of asymptotic stabilization for a class of differential inclusions is considered. The problem of choosing the Lyapunov functions from the parametric class of polynomials for differential inclusions is reduced to that of searching saddle points of a suitable function. A numerical algorithm is used for this purpose. All the results thus obtained can be extended to cover the discrete systems described by difference inclusions.},
author = {Vadim Azhmyakov},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {differential inclusions; difference inclusions; Lyapunov function; asymptotic stability; asymptotic stabilization; polynomial Lyapunov functions},
language = {eng},
number = {1},
pages = {51-62},
title = {A constructive method for solving stabilization problems},
url = {http://eudml.org/doc/271557},
volume = {20},
year = {2000},
}
TY - JOUR
AU - Vadim Azhmyakov
TI - A constructive method for solving stabilization problems
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2000
VL - 20
IS - 1
SP - 51
EP - 62
AB - The problem of asymptotic stabilization for a class of differential inclusions is considered. The problem of choosing the Lyapunov functions from the parametric class of polynomials for differential inclusions is reduced to that of searching saddle points of a suitable function. A numerical algorithm is used for this purpose. All the results thus obtained can be extended to cover the discrete systems described by difference inclusions.
LA - eng
KW - differential inclusions; difference inclusions; Lyapunov function; asymptotic stability; asymptotic stabilization; polynomial Lyapunov functions
UR - http://eudml.org/doc/271557
ER -
References
top- [1] N.N. Krasovskii, Stability of Motion, Stanford University Press, Stanford, CA 1963. Zbl0109.06001
- [2] A.F. Filippov, Stability for differential equations with discontinuous and many-valued right-hand sides, Differents. Uravn. 15 (1979), 1018-1027. Zbl0432.34032
- [3] M. Kisielewicz, Differential Inclusions and Optimal Control, PWN-Kluver Acad. Publ., Dordrecht 1991. Zbl0731.49001
- [4] V. Boltyanski, H. Martini and V. Soltan, Geometric Methods and Optimization Problems, Kluver Academic Publishers, Dordrecht 1999. Zbl0933.90002
- [5] A.F. Filippov, Differential Equations with Discontinuous Right-Hand Side, Nauka, Moskow 1983. (in Russian) Zbl0138.32204
- [6] J.P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin 1984.
- [7] A.P. Molchanov and Ye.S. Pyatnitskiy, Absolute instability of nonlinear nonstationary systems, Automation and Remote Control 43 (1982), 147-157.
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