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

Sufficient conditions for absolute stability and dissipativity of continuous-time recurrent neural networks with two hidden layers are presented. In the autonomous case this is related to a Lur'e system with multilayer perceptron nonlinearity. Such models are obtained after parametrizing general nonlinear models and controllers by a multilayer perceptron with one hidden layer and representing the control scheme in standard plant form. The conditions are expressed as matrix inequalities and can be employed for nonlinear H/sub /spl infin// control and imposing closed-loop stability in dynamic backpropagation.