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First book to comprehensively study a counterpart of classical Lyapunov theory for linear delay free systems
Provides a comprehensive study of Lyapunov matrices for time-delay systems, including existence and computation issues
Includes various applications of the complete type functionals
May be used as a supplemental text for graduate courses in automatic control
Stability is one of the most studied issues in the theory of time-delay systems, but the corresponding chapters of published volumes on time-delay systems do not include a comprehensive study of a counterpart of classical Lyapunov theory for linear delay free systems. The principal goal of the book is to fill this gap, and to provide readers with a systematic and exhaustive treatment of the basic concepts of the Lyapunov-Krasovskii approach to the stability analysis of linear time-delay systems.
The book is organized into two parts. The first part is dedicated to the case of retarded type time-delay systems; it consists of four chapters, which respectively deal with results concerning the existence and uniqueness of the solutions of an initial value problem, the class of linear systems with one delay, the case of systems with several delays, and the case of systems with distributed delays. The second part of the book studies the case of neutral type time-delay systems, containing three chapters that extend the results presented earlier in the book to neutral time-delay systems and treating special classes of linear time-delay systems.
Time-Delay Systems: Lyapunov Functionals and Matrices will be of great use and interest to researchers and graduate students in automatic control and applied mathematics as well as practicing engineers involved in control system design.
Content Level »Research
Keywords »Lyapunov functionals - Lyapunov matrices - Lyapunov-Krasovskii approach - complete type functional - exponential stability - time-delay systems