IEEE Access Special Section: Analysis and Synthesis of Time-Delay System

Time-delay is unavoidable, encountered in many practical systems such as networked control systems, communication networks, manufacturing, and biology. On the one hand, it often represents a source of instability and oscillation. On the other hand, the appearance of delay can have a stabilizing effect, and delayed feedback control can be used to stabilize some unstable systems. Considering its theoretical and practical importance, increasing attention has been focused on the analysis and synthesis of time-delay systems, and various new approaches have been proposed to reduce their conservatism. The aim of reducing the conservatism of delay-dependent stability criteria is to establish new stability criteria to provide a maximal allowable delay as large as possible. Among different techniques, the reduced conservatism is mainly obtained by constructing an improved Lyapunov functional and employing a tighter bound on some weighted cross products. A great number of effective methods have been provided such as delay-partitioning method, convex combination method, Wirtinger-based inequality, and Bessel–Legendre inequality.