Global asymptotic stability criteria for multilayer recurrent neural networks with applications to modelling and control

Sufficient conditions for global asymptotic stability of discrete time multilayer recurrent neural networks are derived in this paper. Both the autonomous and nonautonomous case are treated. Multilayer recurrent neural networks are interpreted as so-called NL_q systems, which are nonlinear systems consisting of an alternating sequence of linear and static nonlinear operators that satisfy a sector condition (q `layers´). It turns out that many problems arising in recurrent neural networks and system and control theory can be interpreted as NL_q systems, such as multilayer Hopfield nets, locally recurrent globally feedforward networks, generalized cellular neural networks, neural state space control systems, the Lur´e problem, linear fractional transformations with real diagonal uncertainty block, digital filters with overflow characteristic etc. In this paper we discuss applications of the theorems for designing neural state space control systems (emulator approach). Narendra´s dynamic backpropagation procedure is modified in order to assess closed loop stability. The new theory also enables to consider reference inputs belonging to the class of functions l₂ instead of specific reference inputs