Criterion for limit cycle-free state-space digital filters with external disturbances and generalized overflow non-linearities

This paper investigates the problem of [Formula: see text] elimination of overflow oscillations in fixed-point state-space digital filters using generalized overflow non-linearities and external disturbance. The generalized overflow non-linearities under consideration cover the common types of overflow arithmetic used in practice, for instance zeroing, two’s complement, triangular and saturation. New criteria are established to ensure not only exponential stability, but also reduction in the effect of external disturbance to an [Formula: see text] norm constraint. The obtained criteria are in linear matrix inequality (LMI) framework and, hence, are computationally tractable. The presented approach constitutes a generalization over several previously reported approaches for the [Formula: see text] elimination of overflow oscillations. For saturation non-linearities, the presented result turns out to be less conservative than several existing criteria. Numerical examples are provided to demonstrate the effectiveness of the presented approach.