Stability Analysis of Linear Systems With Interval Time-Varying Delay

Abstract

In this paper, the problem about stability of system with a time delay is investigated. The time delay is varying in an interval and its derivative is unknown. An augmented Lyapunov-Krasovskii functional (LKF) with considering the time-varying delay is constructed. By augmenting several vectors and introducing some variable-augmented-based free-weighting matrices (FWM), quadric terms or higherorder terms concerning the time-varying delay can be avoided appearance in the bound of the LKF derivative. Thus, the derived stability condition is presented in the form of the linear matrix inequality (LMI), which can be easily checked by existing LMI tools. 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.INDEX TERMS Stability analysis, Time-varying delay, Lyapunov-Krasovskii functional, Free-weighting matrices.