Realizability Condition for Digital Filters With Time Delay Using Generalized Overflow Arithmetic

This brief investigates the input-to-state stability problem of digital filters in the presence of both external disturbance and time delay using generalized overflow arithmetic. A sufficient condition, under which the considered digital filter is realizable and input-to-state stable, is first derived with the help of a tighter matrix inequality. Next, based on this realizability condition, an asymptotic stability criterion is obtained. It is shown that the proposed criterion is less conservative than some existing results. Then two numerical examples are presented to demonstrate the efficiency of the obtained realizability condition and stability criterion.