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.