NEW CONDITIONS FOR GLOBAL STABILITY OF NEURAL NETWORKS WITH APPLICATION TO LINEAR AND QUADRATIC-PROGRAMMING PROBLEMS

In this paper, we present new conditions ensuring existence, uniquenes s, and Global Asymptotic Stability (GAS) of the equilibrium point for a large class of neural networks, The results are applicable to both s ymmetric and nonsymmetric interconnection matrices and allow for the c onsideration of all continuous nondecreasing neuron activation functio ns, Such functions may be unbounded (but not necessarily surjective), may have infinite intervals with zero slope as in a piece-wise-linear model, or both, The conditions on GAS rely on the concept of Lyapunov Diagonally Stable (or Lyapunov Diagonally Semi-Stable) matrices and ar e proved by employing a class of Lyapunov functions of the generalized Lur'e-Postnikov type, Several classes of interconnection matrices of applicative interest are shown to satisfy our conditions for GAS, In p articular, the results are applied to analyze GAS for the class of neu ral circuits introduced in [10] for solving linear and quadratic progr amming problems. In this application, the principal result here obtain ed is that the networks in [10] are GAS also when the constraint ampli fiers are dynamical, as it happens in any practical implementation.