Further refinements in stability conditions for time-varying delay systems

摘要

This paper addresses the problem of assessing the stability of linear time-invariant (LTI) systems with time-varying delay. The first contribution is a new stability criterion specified as a negativity condition for a quadratic function parameterized by the delay. This result mainly follows from an augmented affine parameter-dependent Lyapunov-Krasovskii functional, which, in turn, takes advantages of convexity properties. Then, as a second contribution, we invoke a result from robust control literature to show how the proposed stability condition can be checked exactly in terms of linear matrix inequality (LMI) conditions. The improvements obtained by the proposed refinements are illustrated via numerical examples drawn from the literature.