Realization of Two's Complement Overflow Oscillation-Free 2D Lipschitz Nonlinear Digital Filters

When two-dimensional (2D) digital filters are implemented on finite wordlength processors such as field-programmable gate arrays, microcontrollers and digital signal processing kits, and so on, nonlinearities owing to overflow and quantization are frequently generated. Nonlinearities of this type can lead to instability in the realized 2D digital filters. In practice, the digital filters may also have inherent system nonlinearities. The global asymptotic stability (GAS) problem for a fixed-point 2D Lipschitz nonlinear digital filter (LNDF) represented by the Roesser model with two's complement overflow (TCO) arithmetic is addressed in this paper. A new computationally tractable GAS criterion for such LNDFs is proposed, based on Lyapunov theory, the Lipschitz condition and a TCO arithmetic property. In addition, an improved criterion for the GAS of a 2D digital filter (in the absence of intrinsic system nonlinearities) with TCO arithmetic is presented. The criteria can be used for overflow oscillation-free realization of digital filters with TCO arithmetic. Several examples and simulation results are provided to highlight the potential of stated criteria.