Deterministic and Stochastic Time-Delay Systems

"...the book is in my opinion especially suited to people who already work in the field of delay equations and want to have a good understanding of the Lyapunov approach and to people who are familiar with Lyapunov based control methods for systems without delay and are interested in the extension to time-delay systems. ...The book ends with some appendices, which provide the necessary background to make the book self-contained. Especially the first appendix is interesting, since it not only introduces the reader to linear matrix inequalities, but also explains with some examples how the latter can be numerically solved with the Matlab(R) LMI toolbox." -Bulletin of the Belgian Mathematical Society "The monograph is devoted to problems of stability and stabilization of systems with deviating arguments. It consists of two parts. The first part considers deterministic systems... The second part of the monograph is devoted to similar problems for stochastic systems... Each section has numerous examples that illustrate the results of the obtained theorems. The monograph can be useful for solving concrete problems of stabilization and control theory. Examples of such problems are given at the beginning of the book." -Zentralblatt Math "The book is structured into two parts [Part I: Deterministic Control; Part II: Stochastic Control]. The Introduction presents some dynamical time-delay systems and gives the notations used in the book, states the problems and the difference between the two systems under discussion... Different design algorithms for state feedback are proposed... The LMI framework is used in all problems... [S]everal appendices are included to make the book self-contained. Most of the results are illustrated by numerical examples, solved with the LMI Matlab toolbox. This book can be used either as a text for graduate students in engineering or as a reference for practicing control engineers, graduate students and researchers in control engineering." -Applications of Mathematics

• 1 Introduction.- 1.1 Examples.- 1.2 Notation and Abbreviations.- 1.3 Dynamical Systems with Time Delay.- 1.4 Outline of the Book.- 1.5 Notes.- I Deterministic Control.- 2 Deterministic Time Delay Systems.- 3 Stability and Stabilizability.- 4 Robust Stability and Robust Stabilizability.- 5 H?Control and Filtering.- 6 Robust H?Control, Filtering, and Guaranteed Cost Control.- II Stochastic Control.- 7 Stochastic Time Delay Systems.- 8 Stability and Stabilizability of Markov Jump Systems.- 9 Robust Stability and Stabilizability of Jump Linear Uncertain Systems with Time Delay.- 10 H?Control and Filtering Problems for Markov Jump Systems with Time Delay.- 11 Robust H?and Guaranteed Cost Control for Jump Linear Systems with Time Delay.- 12 Nonlinear Stochastic Control Problem.- A Linear Matrix Inequality and Preliminary Lemmas.- B Matrix Inversion Formulas.- C Kronecker Product.- D Markov Process.- References.