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.