Robust state-space realizations of discrete-time systems against finite word length errors

In this paper, a novel class of robust state-space realizations, called normal realizations, is derived for reducing roundoff noise and self-sustained oscillations which ultimately can not be avoided in real-time applications. It is shown that these realizations are free of limit cycles. Another interesting property of the normal realizations is that they yield a minimal error propagation gain. This class is characterized and the optimal realization problem, defined as to find those normal realizations that minimize roundoff noise gain, is solved analytically. A design example is presented to demonstrate the behavior of the optimal normal realizations and to compare them with several well-known digital filter realizations in terms of minimizing roundoff noise and error propagation.