The second edition of this monograph provides a comprehensive and updated treatment of the analysis of time-delay systems – dynamical systems whose behavior depends on both current and past states – with a primary emphasis on stability and robust stability. It brings together frequency-domain, time-domain, neutral-system, and input–output approaches within a unified framework, covering topics ranging from classical stability criteria and Lyapunov–Krasovskii methods to robust stability under uncertainty, delay-independent analysis, and computational techniques based on linear matrix inequalities. New to this edition is a comprehensive six-chapter treatment of neutral time-delay systems, an area that has seen substantial research activity since publication of the first edition.

Combining fundamental theory with computational tools, illustrative examples, and detailed notes on the research literature, this text will serve both as a reference for researchers and practitioners and as a resource for graduate students seeking a rigorous introduction to time-delay systems and their applications.

Keqin Gu received his BS and MS degrees in Mechanical Engineering from Zhejiang University in 1982 and 1985, respectively, and PhD from Georgia Institute of Technology in 1988. He spent most of his academic career as a faculty member of Mechanical Engineering at Southern Illinois University Edwardsville, where he is currently a Distinguished Research Professor Emeritus. He has been an active contributor in the control systems area, especially on systems with time delays. He had been an Associate Editor or Editorial Board member for a number of premium journals in the field. Due to his contributions to the stability analysis of time-delay systems, he received IFAC Linear Systems Committee “Delay Systems Life-Time Achievement Award” in 2025.

Vladimir L. Kharitonov started his university education at Belarusian State University. He transferred to Leningrad State University and enrolled in Faculty of applied mathematics and control processes, which was newly established by the eminent scientist Vladimir Ivanovich Zubov, who became his supervisor. After graduating in 1973, he became an engineer and researcher at the Laboratory of control devices and mechanisms of Leningrad State University. During that time, in his PhD thesis, he developed a theorem on the robust stability of polynomials, which later had been known as the Kharitonov Theorem. During 1980-1995, he was a faculty member at Leningrad State University (known as Saint Petersburg State University later). He spent the following 11 years at the CINVESTAV, Mexico, and returned to Saint Petersburg State University in 2006, where he retired in 2019. He authored more than 100 research papers and 2 monographs. He served on the editorial boards of several journals including Systems & Control Letters. Due to his pioneering contributions to stability analysis and control of time-delay systems, he received IFAC Linear Systems Committee “Delay Systems Life-Time Achievement Award” in 2021. 

Jie Chen received BS degree in aerospace engineering from Northwestern Polytechnic University, China in 1982, MSE degree in electrical engineering, MA degree in mathematics, and PhD degree in electrical engineering, all from University of Michigan, in 1985, 1987, and 1990, respectively. He was with Department of Electrical Engineering, University of California, Riverside, 1994-2014, where he later became the department chair. Since then, he has been a Chair Professor in Department of Electrical Engineering, City University of Hong Kong, China. He served IEEE and IFAC communities in several leadership roles, on numerous journal editorial boards, and on conference program and organizing committees. He has co-authored several books and contributed to broad areas of research including mathematical systems theory, modeling and system identification, robust control, optimization, time-delay systems, networked control, PID control, cyberphysical systems security, and multi-agent systems. For his contributions, he was recognized by several awards and elected to Fellow of IEEE, AAAS, IFAC, AAIA, and SIAM.