Research output: Contribution to journal › Article › peer-review
Popov-like criterion for the complex-variable systems. / Lipkovich, M. M.; Fradkov, A. L.
In: IFAC-PapersOnLine, Vol. 50, No. 1, 2017, p. 8157-8162.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Popov-like criterion for the complex-variable systems
AU - Lipkovich, M. M.
AU - Fradkov, A. L.
PY - 2017
Y1 - 2017
N2 - A frequency-domain absolute stability conditions for complex-valued Lurie systems with several nonholonomic nonlinearities is given. Graphs of nonlinearities belong to the complex analog of sector. Obtained conditions are sufficient for existence of a Popov-like Lyapunov function from the class "quadratic form plus real part of integral of nonlinearity". Conditions can be viewed as a generalization of Popov criterion to the complex case.The proof is based on the seminal Kalman-Yakobovich-Popov lemma (KYP-lemma) which also holds for the complex case.Obtained stability criterion applied to stability analysis of complex-valued convolutional neural network (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
AB - A frequency-domain absolute stability conditions for complex-valued Lurie systems with several nonholonomic nonlinearities is given. Graphs of nonlinearities belong to the complex analog of sector. Obtained conditions are sufficient for existence of a Popov-like Lyapunov function from the class "quadratic form plus real part of integral of nonlinearity". Conditions can be viewed as a generalization of Popov criterion to the complex case.The proof is based on the seminal Kalman-Yakobovich-Popov lemma (KYP-lemma) which also holds for the complex case.Obtained stability criterion applied to stability analysis of complex-valued convolutional neural network (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
KW - Absolute stability
KW - Lyapunov function
KW - complex variables
KW - frequency domains
KW - nonlinear systems
KW - nonlinearity
KW - LYAPUNOV FUNCTION
KW - CIRCLE CRITERION
KW - STABILITY
KW - EXISTENCE
UR - http://www.scopus.com/inward/record.url?scp=85031777811&partnerID=8YFLogxK
U2 - 10.1016/j.ifacol.2017.08.1262
DO - 10.1016/j.ifacol.2017.08.1262
M3 - статья
AN - SCOPUS:85031777811
VL - 50
SP - 8157
EP - 8162
JO - IFAC-PapersOnLine
JF - IFAC-PapersOnLine
SN - 2405-8963
IS - 1
Y2 - 9 July 2017 through 14 July 2017
ER -
ID: 37787410