An LMI based criterion for the global asymptotic stability of 2-D discrete state-delayed systems with saturation nonlinearities

This paper deals with the problem of global asymptotic stability of a class of two-dimensional (2-D) discrete systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model in presence of saturation nonlinearities and state delays in each of the two independent directions of information propagation. A linear matrix inequality (LMI) based criterion for the global asymptotic stability of such systems is presented. It is shown that several previously reported stability criteria for 2-D discrete FMSLSS model with saturation nonlinearities are recovered from the presented approach as special cases.