Literature Cited
A. Kh. Gelig, G. A. Leonov, and V. A. Yakubovich, The Stability of Nonlinear Systems with a Nonunique Equilibrium State [in Russian], Nauka, Moscow (1978).
Ya. É. Tsypkin, “Criteria of the absolute stability of impulse automatic systems with monotonic characteristics of a nonlinear element,” Dokl. Akad. Nauk SSSR,155, No. 5, 1029–1032 (1964).
K. S. Narendra and Y. S. Cho, “Stability analyses of nonlinear and time-varying discrete systems,” SIAM J. Control,6, No. 4, 625–646 (1968).
R. P. O'Shea and M. I. Younis, “A frequency-time domain stability criterion for sampled-data systems,” Trans. IEEE Autom Control,AC12, No. 6, 719–724 (1967).
E. I. Jury and B. W. Lee, “On the stability of a certain class of nonlinear sampleddata systems,” Trans. IEEE Autom. Control,AC9, No. 1, 51–61 (1964).
V. A. Yakubovich, “Frequency conditions of absolute stability of control systems with several linear or nonlinear nonstationary blocks,” Avtomat. Telemekh., No. 6, 5–30 (1967).
Ya. É. Tsypkin, “On the stability in the whole of nonlinear impulse automatic systems,” Dokl. Akad. Nauk SSSR,145, No. 1, 52–55 (1962).
M. G. Krein and A. A. Nudel'man, The Markov Moment Problem and Extremal Problems [in Russian], Nauka, Moscow (1973).
A. V. Lipatov, “The stability of a discrete stationary system with one block,” Avtomat. Telemekh., No. 9, 74–83 (1984).
Additional information
Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 2, pp. 3–13, March–April, 1989.
Rights and permissions
About this article
Cite this article
Barabanov, N.E. Graph-analytic criteria of stability and instability in large stationary sets of discrete systems. Sib Math J 30, 171–179 (1989). https://doi.org/10.1007/BF00971371
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00971371