Delay and delay-derivative dependent stability analysis for linear time delay systems with a cyclical delay

This study investigates the stability analysis of linear systems with cyclical delays, where the delay interval is partitioned into subintervals that exhibit alternating cycles of monotonic increase and decrease. The Lyapunov-Krasovskii functionals (LKFs) are constructed by integrating two-loop functional frameworks based on delay product terms, which strategically leverage distinct delay monotonicity intervals. A novel delay-derivative-dependent inequality is proposed, which incorporates delay-derivative information into the stability analysis framework. By integrating the proposed delay-product-dependent LKFs with a new negative-definiteness condition (NDC) for generalized bivariate matrix polynomials, an improved stability criterion is described in the form of a linear matrix inequality (LMI). Three numerical examples demonstrate that the derived stability condition is less conservative than previous work.