Stability analysis of layered digital dynamic networks using dissipativity theory

The purpose of this paper is to describe how dissipativity theory can be used for the analysis of discrete-time recurrent neural networks. Using dissipativity theory, we have found conditions for the globally asymptotic stability of equilibrium points of Layered Digital Dynamic Networks (LDDNs), a very general class of recurrent neural networks. We assume that the weights and biases of the LDDN are fixed, the inputs to the LDDN are constant, and there exists an equilibrium point. The LDDNs are then transformed into a standard interconnected system structure. Finally, a fundamental theorem describing the stability of interconnected dissipative systems is applied. The theorem leads to several new sufficient conditions for the stability of equilibrium points for LDDNs. These conditions are demonstrated on several test problems and compared to previously proposed stability conditions. The techniques described here can be applied to the design of neural network controllers and can also be used to provide constraints for recurrent network training.