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

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.