An extended reciprocally convex matrix inequality and its application to stability analysis of systems with additive time-varying delays

摘要

This paper is concerned with the stability analysis of systems with additive time-varying delays. First, an extended reciprocally convex matrix inequality is presented, which is a generalization of the existing reciprocally convex matrix inequalities. Second, combining the proposed matrix inequality with the Wirtinger-based integral inequality, a new stability criterion of systems with additive time-varying delays is proposed. Meanwhile, an improved stability criterion of systems with a single time-varying in a range is also obtained. Finally, two numerical examples are employed to illustrate the advantage of the obtained theoretical results. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.