Two´s complement quantization in two-dimensional state-space digital filters

Two-dimensional (2-D) state-space digital filters are investigated for stability with and without quantization. A sufficient condition is obtained for the stability of the linear Fornasini-Marchesini (1976) state-space model. The same model is then studied for stability when implemented using two´s complement truncation quantization, and a sufficient condition for asymptotic stability of the nonlinear filter is obtained. In the process, a theorem is proved which gives a sufficient condition for the stability of a one-dimensional (1-D) state-space digital filter under the same type of quantization