A Unified Approach to the Stability of Generalized Static Neural Networks With Linear Fractional Uncertainties and Delays

In this paper, the robust global asymptotic stability (RGAS) of generalized static neural networks (SNNs) with linear fractional uncertainties and a constant or time-varying delay is concerned within a novel input-output framework. The activation functions in the model are assumed to satisfy a more general condition than the usually used Lipschitz-type ones. First, by four steps of technical transformations, the original generalized SNN model is equivalently converted into the interconnection of two subsystems, where the forward one is a linear time-invariant system with a constant delay while the feedback one bears the norm-bounded property. Then, based on the scaled small gain theorem, delay-dependent sufficient conditions for the RGAS of generalized SNNs are derived via combining a complete Lyapunov functional and the celebrated discretization scheme. All the results are given in terms of linear matrix inequalities so that the RGAS problem of generalized SNNs is projected into the feasibility of convex optimization problems that can be readily solved by effective numerical algorithms. The effectiveness and superiority of our results over the existing ones are demonstrated by two numerical examples.