Global model of neural networks, stability and learning

A unified state-space representation of dynamical NN models, leading to a global NN vector-matricial state-space model of multilayer NN, is proposed. That NN model will be stable if system eigenvalues have negative real parts. A discrete version of NN model state-space equations, is also given. The behavior of that discrete-time model depends on the period of discretization. The discrete NN model will be stable if system eigenvalues are inside the unit circle. Method for transformation of the global discrete NN model in matrix-vectorial regression form, is given. Applying the square-root matricial identification method for NN learning, it is easy to obtain global stability of the learned NN. The applied learning method gives us the possibility to obtain simultaneously the parameters of mathematical models of different order. It is possible to choose the most appropriate model order by means of the obtained mean square learning error.