Stability Analysis for Time-Delay Systems via a New Negativity Condition on Quadratic Functions

Abstract

This article studies the stability problem of linear systems with time-varying delays. First, a new negative condition is established for a class of quadratic functions whose variable is within a closed set. Then, based on this new condition, a couple of stability criteria for the system under study are derived by constructing an appropriate Lyapunov–Krasovskii functional. Finally, it is demonstrated through two numerical examples that the proposed stability criteria are efficient and outperform some existing methods.

Keywords

• stability
• time-delay systems
• linear matrix inequality (LMI)
• Lyapunov–Krasovskii functional