Neural networks of positive systems

Some definitions and theorems concerning positive continuous-time and discrete-time linear systems are presented. The notion of a positive estimator maping a positive cone into a positive cone is introduced. A multi-layer perceptron and a radial neural network approximating the nonlinear estimator are proposed. A neural network modeling the dynamics of a positive nonlinear dynamical system is also proposed. The new neural networks are verified and illustrated by an example.