Relaxed mixed convex combination lemmas: Application to stability analysis of time-varying delay systems

Abstract

Stability analysis of time-varying delay systems is a fundamental issue, and reducing the conservatism of stability criteria is the key. The high-order Bessel-Legendre inequality together with appropriate Lyapunov-Krasovskii functional (LKF) has the potential to reduce conservatism, but the reciprocally convex and quadratic correlation terms of time-varying delay appear in LKF derivative. This paper proposes the relaxed mixed convex combination lemmas, in which the reciprocally convex combination lemma introduces delay square terms in the LKF derivative, and the quadratic convex combination lemma relaxes the negativity condition for quadratic polynomial functions. The less conservative stability criteria of systems with time-varying delay satisfying two cases are derived, making the delay upper bound larger, and the design degree of freedom higher. Finally, two well-known numerical examples are presented to demonstrate the superiority of the lemmas and criteria over the previous works.