An approach to stability criteria of neural-network control systems

This paper discusses stability of neural network (NN)-based control systems using Lyapunov approach. First, it is pointed out that the dynamics of NN systems can be represented by a class of nonlinear systems treated as linear differential inclusions (LDI). Next, stability conditions for the class of nonlinear systems are derived and applied to the stability analysis of single NN systems and feedback NN control systems. Furthermore, a method of parameter region (PR) representation, which graphically shows the location of parameters of nonlinear systems, is proposed by introducing new concepts of vertex point and minimum representation. From these concepts, an important theorem, which is useful for effectively finding a Lyapunov function, is derived. Stability criteria of single NN systems are illustrated in terms of PR representation. Finally, stability of feedback NN control systems, which consist of a plant represented by an NN and an NN controller, is analyzed.