NL(sub)q theory: unifications in the theory of neural networks, systems and control

摘要

The aim of this paper is to present some results on NL(sup)q theory, a new theory that originated from the study of stability criteria for neural state space control system. NL(sub)q s represent a large class of nonlinear dynamical systems in state space form and contain a number of q layers of an alternating sequence of linear and nonlinear operators that satisfy a sector condition. NL(sub)q s have many special cases in neural networks, systems and control. Among the examples are e.g. the Hopfield network, Generalized Cellular Neural Networks, Locally Recurrent Globally Feedforward neural networks, Neural state space control systems, Linear Fractional Transformations with real diagonal uncertainty block, the Lur'e problem and digital filters with overflow characteristic. Within NL(sub)q theory sufficient conditions for global asymptotic stability, input-output stability and dissipativity are available. Certain results for q=1 reduce to well-known results in modern control theory (H(sub) infinite theory and mu theory).