Refined Reciprocally Convex Inequality for Less Conservative Stability Analysis of Systems with Interval Delay

This paper investigates problems related to the stability of time-varying delay systems using three new inequality lemmas. A constrained matrix inequality lemma and an unconstrained one, both of which concern high-order reciprocally convex combination, are proposed for analyzing asymptotic stability of the delayed system for networked control. A necessary and sufficient condition lemma is also established to ensure the negative definiteness of high-order matrix polynomials. A novel augmented Lyapunov-Krasovskii functional (LKF) with a third-order matrix polynomial on the interval delay is constructed to generate quartic matrix polynomials. The proven lemmas are exploited for the time derivative of LKF to expound delay-dependent stability criteria with reduced conservatism. Finally, a numerical example is presented to demonstrate the effectiveness and superiority of the raised criteria.