A novel word length selection method for a guaranteed H_∞ interference rejection performance and overflow oscillation-free realization of 2-D digital filters

This paper examines the problem of the local overflow stability and disturbance attenuation performance analysis of two-dimensional (2-D) Roesser digital filters in the presence of external interferences. In particular, by utilizing the local properties of saturation nonlinearity and Lyapunov stability theory, a novel linear matrix inequality (LMI)-based condition is proposed that not only ensures the nonexistence of overflow oscillations, but also yields the H_∞ interference rejection performance of 2-D digital filters under the overflow constraint. It is worth mentioning here that in contrast to the traditional approaches based on modeling the saturation with a global sector-bound condition, the proposed approach provides a less conservative bound for the attenuation of disturbances and renders the idea of minimum word length for realizing the 2-D (Roesser) filter to eliminate overflow oscillations and attain the specified H_∞ interference attenuation performance index. Finally, a numerical simulation example is also provided, which demonstrates the superiority of the proposed method over the existing techniques.