Lur'e systems with multilayer perceptron and recurrent neural networks: Absolute stability and dissipativity

Sufficient conditions for absolute stability and dissipativity of continuou s-time recurrent neural networks with two hidden layers are presented. In t he autonomous case this is related to a Lur'e system with multilayer percep tron nonlinearity. Such models are obtained after parameterizing general no nlinear models and controllers by a multilayer perceptron with one hidden l ayer and representing the control scheme in standard plant Form. The condit ions are expressed as matrix inequalities and can be employed for nonlinear Ii, control and imposing closed-loop stability in dynamic back propagation .