A current neural network is said to be completely stable if its state trajectory converges to an equilibrium point for any initial condition. The author recently derived a sufficient condition for recurrent neural networks with the piecewise linear output function to be completely stable. In this report, a new complete stability condition which is a generalization of the above mentioned sufficient condition is given. A convergence theorem of the Gauss-Seidel method, which is a well-known iterative technique for solving linear algebraic equations, plays an important role while most of the conventional stability criteria were obtt1tried by constructing Lyapunov functions.
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