Low dimensional conditions for global asymptotic stability of M-D nonlinear digital filters

The problem of global asymptotic stability in nonlinear recursive digital m-D filters with a first hyper-quadrant causality structure is addressed. Necessary 1-D conditions, which are simple to check, are derived in the form of m 1-D nonlinear system equations. Generalizations to ν-dimensional (ν<m) subsystems are also provided. These derived conditions are useful in determining asymptotic convergence of m-D digital filters implemented in fixed or floating point arithmetic. The set of one-dimensional conditions can be considered the analogous result to practical BIBO stability for linear m-D systems