In the mathematical description of a physical or biological process, it is a common practice \0 assume that the future behavior of Ihe process considered depends only on the present slate, and therefore can be described by a finite sct of ordinary diffe­ rential equations. This is satisfactory for a large class of practical systems. However. the existence of lime-delay elements, such as material or infonnation transport, of­ tcn renders such description unsatisfactory in accounting for important behaviors of many practical systems. Indeed. due largely to the current lack of effective metho­ dology for analysis and control design for such systems, the lime-delay elements arc often either neglected or poorly approximated, which frequently results in analysis and simulation of insufficient accuracy, which in turns leads to poor performance of the systems designed. Indeed, it has been demonstrated in the area of automatic control that a relatively small delay may lead to instability or significantly deteriora­ ted perfonnances for the corresponding closed-loop systems.

I Basic Theory.- Basic Theory for Linear Delay Equations.- II Stability and Robust Stability.- Complete Type Lyapunov-Krasovskii Functionals.- Robust Stability Conditio ns of Quasipolynomials by Frequency Sweeping.- Improvements on the Cluster Treatment of Characteristic Roots and the Case Studies.- From Lyapunov-Krasovskii Functionals for Delay-Independent Stability to LMI Conditions for µ-Ana1ysis.- III Control, Identification, and Observer Design.- Finite Eigenstructure Assignment for Input Delay Systems.- Control of Systems with Input Delay-An Elementary Approach.- On the Stabilization of Systems with Bounded and Delayed Input.- Identifiability and Identification of Linear Systems with Delays.- A Model Matching Solution of Robust Observer Design for Time-Delay Systems.- IV Computation, Software, and Implementation.- Adaptive Integration of Delay Differential Equations.- Software for Stability and Bifurcation Analysis of Delay Differential Equations and Applications to Stabilization.- Empirical Methods for Determining the Stability of Certain Linear Delay Systems.- Stability Exponent and Eigenvalue Abscissas by Way of the Imaginary Axis Eigenvalues.- The Effect of Approximating Distributed Delay Control Laws on Stability.- V Partial Differential Equations, Nonlinear and Neutral Systems.- Synchronization Through Boundary Interaction.- Output Regulation of Nonlinear Neutral Systems.- Robust Stability Analysis of Various Classes of Delay Systems.- On Strong Stability and Stabilizability of Linear Systems of Neutral Type.- Robust Delay Dependent Stability Analysis of Neutral Systems.- VI Applications.- On Delay-Based Linear Models and Robust Control of Cavity Flows.- Active-adaptive Control of Acoustic Resonances in Flows.- Robust Prediction-Dased Control for UnstableDelay Systems.- Robust Stability of Teleoperation Schemes SUbject to Constant and Time-Varying Communication Delays.- Bounded Control of Multiple-Delay Systems with Applications to ATM Networks.- Dynamic Time Delay Models for Load Balancing. Part I: Deterministic Models.- Dynamic Time Delay Models for lA>ad Balancing. Part II: A Stochastic Analysis of the Effect of Delay Uncertainty.- VII Miscellaneous Topics.- Asymptotic Properties of Stochastic Delay Systems.- Stability and Dissipativity Theory for Nonnegative and Compartmental Dynamical Systems with Time Delay.- List of Contributors.