Research output: Contribution to journal › Article › peer-review
On problems of Aizerman and Kalman. / Leonov, G.A.; Kuznetsov, N.V.; Bragin, V.O.
In: Vestnik St. Petersburg University: Mathematics, Vol. 43, No. 3, 2010, p. 148-162.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - On problems of Aizerman and Kalman
AU - Leonov, G.A.
AU - Kuznetsov, N.V.
AU - Bragin, V.O.
PY - 2010
Y1 - 2010
N2 - The problems of the stability of nonlinear control systems posed by Aizerman and Kalman have stimulated the development of methods for detecting hidden periodic oscillations in multidimensional dynamical systems. In the 1950s, Pliss developed an analytical method for detecting periodic oscillations in third-order systems satisfying the generalized Routh-Hurwitz conditions. It has turned out that this generalized method of Pliss can be regarded as a special version of the describing function method in the critical case. Being combined with computational procedures based on applied bifurcation theory, this method makes it possible to obtain new classes of systems for which the conjectures of Aizerman and Kalman are false. The known approaches to constructing counterexamples to Aizerman's and Kalman's conjectures proposed by Fitts, Barabanov, and Llibre are reviewed. A new effective analytical-numerical method for constructing such counterexamples is presented. The method is based on combining the classical theo
AB - The problems of the stability of nonlinear control systems posed by Aizerman and Kalman have stimulated the development of methods for detecting hidden periodic oscillations in multidimensional dynamical systems. In the 1950s, Pliss developed an analytical method for detecting periodic oscillations in third-order systems satisfying the generalized Routh-Hurwitz conditions. It has turned out that this generalized method of Pliss can be regarded as a special version of the describing function method in the critical case. Being combined with computational procedures based on applied bifurcation theory, this method makes it possible to obtain new classes of systems for which the conjectures of Aizerman and Kalman are false. The known approaches to constructing counterexamples to Aizerman's and Kalman's conjectures proposed by Fitts, Barabanov, and Llibre are reviewed. A new effective analytical-numerical method for constructing such counterexamples is presented. The method is based on combining the classical theo
KW - absolute stability
KW - Aizerman conjecture
KW - hidden oscillations
KW - Kalman conjecture
KW - periodic solutions
U2 - 10.3103/S1063454110030052
DO - 10.3103/S1063454110030052
M3 - статья
VL - 43
SP - 148
EP - 162
JO - Vestnik St. Petersburg University: Mathematics
JF - Vestnik St. Petersburg University: Mathematics
SN - 1063-4541
IS - 3
ER -
ID: 5487609