Stability analysis of systems with time-varying delays for conservatism and complexity reduction

This paper is concerned with the stability analysis of systems with time-varying delays via the Lyapunov- Krasovskii functional (LKF) method. Unlike the most existing works primarily on conservatism reduction, this paper aims to establish stability criteria with less conservatism as well as low complexity, based on a relatively simple LKF with improved derivative treatments. For this purpose, a fragmented-component-based integral inequality is developed through matrix-separation and mixed estimation of the augmented integral term, which tights the estimation gap and contributes to conservatism reduction; and a novel linearized transformation method is proposed by stripping-simplification and matrix-injection, which handles nonlinear delay-itself- related terms at a low complexity cost. Then, a novel stability criterion as well as several comparative criteria are obtained for linear time-delay systems. Finally, the superiority of the proposed methods is demonstrated via two benchmark examples and a load frequency control system.