Overflow oscillations-free realization of discrete-time 2D Roesser models under quantization and overflow constraints

This brief proposes novel linear matrix inequalities-based criteria to investigate the asymptotic convergence of states to an overflow oscillations-free ellipsoidal region for a two-dimensional Roesser digital model subjected to quantization and overflow effects of a digital hardware. Existence of a novel region for two-dimensional Rosser systems is shown in the present study, in which overflow oscillations can be completely removed for realization of a system. New realization conditions for Roesser systems in the absence and presence of external interference along with stability and overflow-free regional behavior are investigated by application of regional analysis, convex routines, and Lyapunov redesign. In contrast to existing literature that primarily focus on a specific type of quantitation and global asymptotic stability, the conditions in the presented work are derived by considering the generalized quantization arithmetic and for guaranteeing convergence of states in a convex oscillations-free region (in the steady-state) in both the absence and presence of bounded interference. The localized stable regions can be directly associated with the word-length employed to realize the two-dimensional systems on a digital hardware. Simulation results are also furnished to validate the efficacy of the proposed approach.