A discrete-time looped functional approach and its application to discrete-time systems with cyclically varying delays

This paper investigates the stability analysis problem of discrete-time systems with cyclically varying delays. Unlike previous studies, the delay investigated in this paper cyclically alternates between increasing and decreasing changes within its upper and lower bounds. First, to reasonably describe the cyclic variation characteristics of the delay, a discrete-time looped functional (DTLF) approach and a refined allowable delay set (ADS) are proposed. Then, based on the constructed DTLF with delay-product terms and using matrix-separation-based inequality to estimate its forward difference, delay-variation-interval-dependent stability conditions considering two different ADSs are derived. Finally, the effectiveness and superiority of the obtained conditions are demonstrated through two numerical examples.