Stability Analysis of Linear Systems With Interval Time-Varying Delay

Abstract

In this paper, the problem of stability of systems with a time delay is investigated. The time delay is assumed to vary in an interval, and its derivative is unknown. An augmented Lyapunov-Krasovskii functional (LKF) is constructed considering the time-varying delay fully. By augmenting several vectors and introducing some variable-augmented-based free-weighting matrices (FWMs), quadric terms, or higher-order terms of the time-varying delay do not appear in the derived stability conditions. Thus, the derived stability condition is presented as linear matrix inequalities (LMIs), which existing LMI tools can readily check. Finally, two examples, including a commonly used numerical example and the stability of load-frequency control (LFC) in single-area power systems, are provided to demonstrate the validity and merits of the proposed method.

Keywords

• Stability analysis
• time-varying delay
• Lyapunov-Krasovskii functional
• free-weighting matrices