Asymptotic stability of two-dimensional digital filters with overflow nonlinearities

Lyapunov´s second method is used to establish several sufficient conditions for the global asymptotic stability of the trivial solution of 2D quarter plane state-space digital filters which are endowed with a general class of overflow nonlinearities. The authors´ results are generalized to a class of m-D (multi-dimensional) digital filters endowed with overflow nonlinearities. Two specific examples are considered to demonstrate the applicability of their results