Time delays are important components of many systems in, for instance, engineering, physics, economics, and the life sciences, because the transfer of material, energy, and information is usually not instantaneous. Time delays may appear as computation and communication lags, they model transport phenomena and heredity, and they arise as feedback delays in control loops. This monograph addresses the problem of stability analysis, stabilization, and robust fixed-order control of dynamical systems subject to delays, including both retarded- and neutral-type systems. Within the eigenvalue-based framework, an overall solution is given to the stability analysis, stabilization, and robust control design problem, using both analytical methods and numerical algorithms and applicable to a broad class of linear time-delay systems.? In this revised edition, the authors make the leap from stabilization to the design of robust and optimal controllers and from retarded-type to neutral-type delay systems, thus enlarging the scope of the book within control; include new, state-of-the-art material on numerical methods and algorithms to broaden the book?s focus and to reach additional research communities, in particular numerical linear algebra and numerical optimization; and increase the number and range of applications to better illustrate the effectiveness and generality of their approach.?

The beginning of the 21st century can be characterized as the” time-delay boom” leading to numerous important results. The purpose of this book is two-fold, to familiarize the non-expert reader with time-delay systems and to provide a systematic treatment of modern ideas and techniques for experts. This book is based on the course ”Introduction to time-delay systems” for graduate students in Engineering and Applied Mathematics that the author taught in Tel Aviv University in 2011-2012 and 2012-2013 academic years. The sufficient background to follow most of the material are the undergraduate courses in mathematics and an introduction to control. The book leads the reader from some basic classical results on time-delay systems to recent developments on Lyapunov-based analysis and design with applications to the hot topics of sampled-data and network-based control. The objective is to provide useful tools that will allow the reader not only to apply the existing methods, but also to develop new ones. It should be of interest for researchers working in the field, for graduate students in engineering and applied mathematics, and for practicing engineers. It may also be used as a textbook for a graduate course on time-delay systems.

This book presents up-to-date research developments and novel methodologies to solve various stability and control problems of dynamic systems with time delays. First, it provides the new introduction of integral and summation inequalities for stability analysis of nominal time-delay systems in continuous and discrete time domain, and presents corresponding stability conditions for the nominal system and an applicable nonlinear system. Next, it investigates several control problems for dynamic systems with delays including H(infinity) control problem Event-triggered control problems; Dynamic output feedback control problems; Reliable sampled-data control problems. Finally, some application topics covering filtering, state estimation, and synchronization are considered. The book will be a valuable resource and guide for graduate students, scientists, and engineers in the system sciences and control communities.

This book is a self-contained presentation of the background and progress of the study of time-delay systems, a subject with broad applications to a number of areas.

Time-delay occurs in many dynamical systems such as biological systems, chemical systems, metallurgical processing systems, nuclear reactor, long transmission lines in pneumatic, hydraulic systems and electrical networks. Especially, in recent years, time-delay which exists in networked control s- temshasbroughtmorecomplexproblemintoanewresearcharea.Frequently, itisasourceofthegenerationofoscillation,instabilityandpoorperformance. Considerable e?ort has been applied to di?erent aspects of linear time-delay systems during recent years. Because the introduction of the delay factor renders the system analysis more complicated, in addition to the di?culties caused by the perturbation or uncertainties, in the control of time-delay s- tems, the problems of robust stability and robust stabilization are of great importance. This book presents some basic theories of stability and stabilization of systems with time-delay, which are related to the main results in this book. More attention will be paid on synthesis of systems with time-delay. That is, sliding mode control of systems with time-delay; networked control systems with time-delay; networked data fusion with random delay.

Stability is one of the most studied issues in the theory of time-delay systems, however 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.​ 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.​

The authors have developed a methodology for control of nonlinear systems in the presence of long delays, with large and rapid variation in the actuation or sensing path, or in the presence of long delays affecting the internal state of a system. In addition to control synthesis, they introduce tools to quantify the performance and the robustness properties of the designs provided in the book. The book is based on the concept of predictor feedback and infinite-dimensional backstepping transformation for linear systems and the authors guide the reader from the basic ideas of the concept?with constant delays only on the input?all the way through to nonlinear systems with state-dependent delays on the input as well as on system states. Readers will find the book useful because the authors provide elegant and systematic treatments of long-standing problems in delay systems, such as systems with state-dependent delays that arise in many applications. In addition, the authors give all control designs by explicit formulae, making the book especially useful for engineers who have faced delay-related challenges and are concerned with actual implementations and they accompany all control designs with Lyapunov-based analysis for establishing stability and performance guarantees.

This book provides an introduction to the analysis and control of Linear Parameter-Varying Systems and Time-Delay Systems and their interactions. The purpose is to give the readers some fundamental theoretical background on these topics and to give more insights on the possible applications of these theories. This self-contained monograph is written in an accessible way for readers ranging from undergraduate/PhD students to engineers and researchers willing to know more about the fields of time-delay systems, parameter-varying systems, robust analysis, robust control, gain-scheduling techniques in the LPV fashion and LMI based approaches. The only prerequisites are basic knowledge in linear algebra, ordinary differential equations and (linear) dynamical systems. Most of the results are proved unless the proof is too complex or not necessary for a good understanding of the results. In the latter cases, suitable references are systematically provided. The first part pertains on the representation, analysis and control of LPV systems along with a reminder on robust analysis and control techniques. The second part is concerned with the representation and analysis of time-delay systems using various time-domain techniques. The third and last part is devoted to the representation, analysis, observation, filtering and control of LPV time-delay systems. The book also presents many important basic and advanced results on the manipulation of LMIs.

Time delays exist in many engineering systems such as transportation, communication, process engineering and networked control systems. In recent years, time delay systems have attracted recurring interests from research community. Much of the effort has been focused on stability analysis and stabilization of time delay systems using the so-called Lyapunov-Krasovskii functional together with a linear matrix inequality approach, which provides an efficient numerical tool for handling systems with delays in state and/or inputs. Recently, some more interesting and fundamental development for systems with input/output (i/o) delays has been made using time domain or frequency domain approaches. These approaches lead to analytical solutions to time delay problems in terms of Riccati equations or spectral factorizations. This monograph presents simple analytical solutions to control and estimation problems for systems with multiple i/o delays via elementary tools such as projection. We propose a re-organized innovation analysis approach for delay systems and establish a duality between optimal control of systems with multiple input delays and smoothing estimation for delay free systems. These appealing new techniques are applied to solve control and estimation problems for systems with multiple i/o delays and state delays under both the H2 and H-infinity performance criteria.

This monograph is devoted to the effect of delays on the stability properties of dynamical systems. Stability regions with respect to the delay parameters are considered, and some sufficient characterizations are proposed. This monograph addresses general delay problems and offers solutions in some cases. In other cases, approximations of the stability regions can be proposed. The interpretation of delays as uncertainty allows the authors to use the advances in robust control and robust convex optimization to solve or to approximate the solutions of the corresponding problems.