Comments on "Lur'e systems with multilayer perceptron and recurrent neural networks: absolute stability and dissipativity

In this paper we consider Lur'e systems where a linear dynamical system is feedback interconnected to a multilayer perceptron nonlinearity, corresponding to recurrent neural networks with two hidden layers. For this class of nonlinear systems, we present suu-cient conditions for global asymptotic stability based on quadratic and Lur'e-Postnikov Lyapunov functions. Suucient conditions for dissipativity are derived with respect to a supply rate of quadratic form (including the cases of passivity and nite L 2-gain) and a storage function of quadratic form and quadratic from with integral terms. All derived conditions are expressed as matrix inequalities.