Novel ISS criteria for digital filters using generalized overflow non-linearities and external interference

Abstract

Sufficient criteria for input-to-state stability (ISS) of fixed-point state-space interfered digital filters with generalized overflow non-linearities are presented. The generalized overflow non-linearities under consideration cover the usual types of overflow arithmetic employed in practice, such as saturation, zeroing, two’s complement and triangular. The criteria not only ensure diminishing consequence of external interference but also confirm the asymptotic stability of the system when external interference disappears. The criteria are derived in the linear matrix inequality (LMI) framework. Simulation results are provided to illustrate the utility of the presented approach. With the help of one example, it is illustrated that the presented approach can lead to a less stringent ISS condition for the digital filters with saturation non-linearities compared with a previously reported approach.