Improved delay-dependent stability analysis of digital filters with generalized overflow arithmetic

This paper introduces a new set of conditions that establish Input-to-State Stability (ISS) for digital filters with external disturbance input and time-varying delays, all within the context of generalized overflow arithmetic. A unique augmented Lyapunov function and a novel summation inequality are applied to formulate a new criterion for ISS. This criterion assesses the ISS of digital filters in the presence of external disturbance, enabling the identification of asymptotic stability even in the absence of such disturbance. The criteria are developed using linear matrix inequalities (LMIs). The efficacy of the results is demonstrated through three numerical examples, highlighting that the proposed criteria are less conservative than some recent results.