Literature Cited
M. A. Krasnosel'skii and A. V. Pokrovskii, “The principle of absence of bounded solutions in an absolute stability problem,” Dokl. Akad. Nauk SSSR,233, No. 3, 293–296 (1977).
M. A. Krasnosel'skii and A. V. Pokrovskii, “The principle of absence of bounded solutions in an absolute stability problem,” Avtomat. Telemekh., No. 2, 42–52 (1978).
V. A. Yakubovich, “Frequency conditions of self-oscillations in nonlinear systems with one stationary nonlinearity,” Sib. Mat. Zh.,14, No. 5, 1100–1129 (1973).
A. Kh. Gelig, G. A. Leonov, and V. A. Yakubovich, Stability of Nonlinear Systems with a Nonunique Equilibrium State [in Russian], Nauka, Moscow (1978).
V. A. Yakubovich, “Absolute instability of nonlinear control systems, I. General frequency criteria,” Avtomat. Telemekh., No. 12, 5–14 (1970).
V. A. Yakubovich, “A frequency theorem in control theory,” Sib. Mat. Zh.,14, No. 2, 384–420 (1973).
C. Corduneanu, Integral Equations and Stability of Feedback Systems, New York-London (1973).
N. E. Barabanov, “A dichotomy of nonlinear control systems that satisfy a differential constraint,” Avtomat. Telemekh., No. 2, 5–7 (1982).
P. Hartman, Ordinary Differential Equations, S. M. Hartman (1973).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 2, pp. 42–49, March–April, 1984.
Rights and permissions
About this article
Cite this article
Barabanov, N.E. Instability of stationary sets of nonlinear systems of differential equations. Sib Math J 25, 200–206 (1984). https://doi.org/10.1007/BF00971457
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00971457