Lyapunov Stability of Two-dimensional Digital Filters with Overrow Nonlinearities

| In the present paper, the Second Method of Lyapunov is utilized to establish suucient conditions for the global asymptotic stability of the trivial solution of zero-input 2{D (two-dimensional) Fornasini-Marchesini state-space digital lters which are endowed with a general class of overrow nonlinearities. Results for the global asymptotic stability of the null solution of the 2{D Fornasini-Marchesini second model with overrow nonlinearities are established. Several classes of Lyapunov functions are used in establishing the present results including vector norms and the quadratic form. When the quadratic form Lyapunov functions are considered, the present results involve necessary and suucient conditions under which positive deenite matrices can be used to generate Lyapunov functions for 2{D digital lters with overrow nonlinearities.