Stability analysis of state regulator systems with finite word length effects

An approach for analyzing the realization of a state regulator system and running on a digital machine by employing a stability criterion is proposed. This permits that equivalent stable state space structures when regarding their input-output characteristics with infinite precision can also perform stably when they are operating on a digital machine with word-length limitations. Both the round off errors occurring in the coefficients and computation errors in additions and multiplications will be pondered in this study. It is shown that based on the Bellman-Grownwall lemma, the stability criterion is derived and a minimum word-length for achieving stability is obtained. Finally, numerical simulations are performed to illustrate the results