An improved reciprocally convex inequality and its application to time-varying delay systems (Q2675096)

The Lyapunov-Krasovskii functional (LKF) method is an effective and popular method for the stability of time-delay differential equations. For a successful applications, some integral inequalities are needed. To deal with time-varying delays, some reciprocally convex inequalities are developed, which can change non convex terms into a single convex expression. In this paper, first an improved reciprocally convex inequality is established, which includes some existing ones as special cases. Then this inequality is used to obtain a stability criterion for a class of linear system of time-varying delay differential equations with constant coefficients. The effectiveness of the stability result is demonstrated by two numerical examples.