A stability analysis of two-dimensional nonlinear digital state-space filters

Two different methods for a stability analysis of 2-D nonlinear discrete state-space systems under zero input conditions are provided. The first method reduces the task of testing a 2-D discrete nonlinear or shift-varying system to a single 2-D linear stability test of a system matrix with nonnegative system matrix entries. The second method is based on a number of norm tests for products of extreme matrices, and can be considered the 2-D counterpart of the method for 1-D systems described by K.T. Erickson and A.N. Michel (1985). Both of the introduced methods are based on the sector description of the nonlinearity and can be used to analyze digital filter stability under finite-word-length effects.>