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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.