Two new criteria for the realization of interfered digital filters utilizing saturation overflow nonlinearity

• New and first criteria for the input-to-state stability (ISS) of digital filters with external interference are proposed.
• The effect of external interference can be attenuated by the ISS property.
• Criteria ensure asymptotic stability without external interference.
• Criteria are represented by linear matrix inequality (LMI).

In this paper, an input-to-state stability (ISS) approach is used to derive two new criteria for the realization of fixed-point state-space and direct-form digital filters with saturation overflow nonlinearity and external interference via augmented Lyapunov functions. The two proposed realization criteria ensure ISS for external interference. Moreover, these criteria guarantee asymptotic stability without external interference. They take the form of linear matrix inequality (LMI) and, hence, are computationally tractable. Illustrative examples demonstrate the effectiveness of the two proposed criteria.