On balanced realizations of 2-D delta-operator formulated discrete-time systems

Delta-operator based implementations can avoid the numerical ill-conditioning usually associated with the high speed shift-operator based implementations of discrete-time systems. Moreover, it provides a unified methodology for tackling both continuous- and discrete-time systems. In particular, it has been shown that, delta-operator based balanced realizations can offer superior coefficient sensitivity properties under fixed-point arithmetic. The authors address computation of balanced realizations. For this purpose, given a discrete-time system, the relationship between its shift- and delta-operator formulated balanced realizations is presented.