Popov-like criterion for the complex-variable systems

M. M. Lipkovich, A. L. Fradkov

Research output


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

Original languageEnglish
Pages (from-to)8157-8162
Number of pages6
Issue number1
Publication statusPublished - 1 Jul 2017

Scopus subject areas

  • Control and Systems Engineering

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