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Delay, Alexandre

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Delay differential equations

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Stability, Control and Application of Time-Delay Systems gives a systematic description of these systems. It includes adequate designs of integrated modeling and control and frequency characterizations. Common themes revolve around creating certain synergies of modeling, analysis, control, computing and applications of time delay systems that achieve robust stability while retaining desired performance quality. The book provides innovative insights into the state-of-the-art of time-delay systems in both theory and practical aspects. It has been edited with an emphasis on presenting constructive theoretical and practical methodological approaches and techniques.

Time delay systems.

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Differential equations --- Oscillations. --- Delay equations.

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In recent years there has been a resurgence of interest in the study of delay differential equations motivated largely by new applications in physics, biology, ecology, and physiology. The aim of this monograph is to present a reasonably self-contained account of the advances in the oscillation theory of this class of equations. Throughout, the main topics of study are shown in action, with applications to such diverse problems as insect population estimations, logistic equations in ecology, the survival of red blood cells in animals, integro-differential equations, and the motion of the tips of growing plants. The authors begin by reviewing the basic theory of delay differential equations, including the fundamental results of existence and uniqueness of solutions and the theory of the Laplace and z-transforms. Little prior knowledge of the subject is required other than a firm grounding in the main techniques of differential equation theory. As a result, this book provides an invaluable reference to the recent work both for mathematicians and for all those whose research includes the study of this fascinating class of differential equations.

Differential equations --- Oscillations. --- Delay equations.