Stability analysis of systems with additive time-varying delays via new bivariate quadratic reciprocally convex inequality

Abstract

This paper focuses on the stability analysis of additive time-varying delay systems. First, a bivariate quadratic reciprocally convex matrix inequality is derived, which serves as a generalization of traditional reciprocally convex inequalities. By applying the Lyapunov–Krasovskii functional method, this matrix inequality is incorporated to form a new stability criterion applicable to systems with additive time-varying delays. Finally, some numerical examples are presented to demonstrate the effectiveness of the theoretical results obtained.

Keywords

• stability
• reciprocally convex inequality
• lyapunov–krasovskii functional method
• additive time-varying delay