ISS Criterion for the Realization of Fixed-Point State-Space Digital Filters with Saturation Arithmetic and External Interference

Abstract

This paper investigates the problem of the input-to-state stability (ISS) of fixed-point state-space digital filters in the presence of saturation overflow arithmetic and external interference. By utilizing an augmented Lyapunov function and the passivity property associated with multiple saturation nonlinearities, a new criterion for the ISS of interfered digital filters with saturation is proposed. When the external interference is present, the criterion can be used to determine ISS of digital filters. Without the external interference, the criterion is capable of detecting the asymptotic stability of digital filters. The proposed ISS criterion is in linear matrix inequality framework and, hence, is computationally tractable. The obtained criterion turns out to be less conservative than a recently reported ISS criterion. The superiority of the presented approach over the existing techniques is confirmed by numerical examples.