L_∞-gain performance analysis for two-dimensional Roesser systems with persistent bounded disturbance and saturation nonlinearity

The l_∞-gain approach has been an essential tool in one-dimensional system theory. However, limited results have been presented in the literature for the two-dimensional (2-D) l_∞-gain approach. This paper investigates the l_∞-gain performance for 2-D systems in the Roesser model with persistent bounded disturbance input and saturation nonlinearity. A linear matrix inequality (LMI)-based condition is established to reduce the effect of persistent bounded disturbance input on 2-D systems within a given disturbance attenuation level based on the discrete Jensen inequality, lower bounds lemma, and diagonally dominant matrices. We apply the obtained results to the l_∞-gain performance analysis for 2-D digital filters with saturation arithmetic.