Synopses & Reviews
Following the recent developments in the field of absolute stability, Professor Xiaoxin Liao, in conjunction with Professor Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and the Lurie control system, before moving on to the simple algebraic sufficient conditions for the absolute stability of autonomous and non-autonomous ODE systems, as well as several special classes of Lurie-type systems. The focus of the book then shifts toward the new results and research that have appeared in the decade since the first edition was published. This includes nonlinear control systems with multiple controls, interval control systems, time-delay and neutral Lurie control systems, systems described by functional differential equations, the absolute stability for neural networks, as well as applications to chaos control and chaos synchronization. This book is aimed at undergraduates and lecturers in the areas of applied mathematics, nonlinear control systems and chaos control and synchronisation, but may also be useful as a reference work for researchers and engineers. The book is self-contained, though a basic knowledge of calculus, linear system and matrix theory, and ordinary differential equations is required to gain a complete understanding of the workings and methodologies discussed within.
Review
From the reviews of the second edition: "This monograph is devoted to stability problems of linear systems with nonlinear feedbacks ... . The monograph is written in a very clear style. It contains many new ideas and it will certainly be useful as a reference work for engineers." (Stanislaw Sedziwy, Mathematical Reviews, Issue 2009 m)
Review
From the reviews of the second edition: "This monograph is devoted to stability problems of linear systems with nonlinear feedbacks ... . The monograph is written in a very clear style. It contains many new ideas and it will certainly be useful as a reference work for engineers." (Stanislaw Sedziwy, Mathematical Reviews, Issue 2009 m) "This book is based heavily on material developed by the authors and is aimed at graduate students and advanced undergraduates. The book begins with an introduction to Lurie control systems, and algebraic sufficient conditions for the absolute stability of several classes of Lurie-type systems are developed. Recent developments are then presented, including results for systems with multiple controls, interval systems, time-delay and neutral Lurie control systems, neural networks, and applications to chaos control and synchronization." (IEEE Control Systems Magazine, Vol. 29, October, 2009)
Synopsis
Following the recent developments in the field of absolute stability, this seminal work on the subject has been updated. It covers the new results and research that have appeared in the decade since the first edition was published.
Table of Contents
1. Introduction.- 2.Principal Theorems on Global Stability.- 3. Sufficient Conditions of Absolute Stability - Classical Methods.- 4. Necessary, and Sufficient Conditions for Absolute Stability.- 5. Special Lurie-Type Control Systems.- 6. Non-Autonomous Systems.- 7. Systems with Multiple Nonlinear Feedback Controls.- 8. Robust Absolute Stability of Interval Control Systems.- 9. Discrete Control Systems.- 10. Time-Delayed and Neutral Lurie Control Systems.- 11. Control Systems Described by Functional Differential Equations.- 12. Absolute Stability of Hopfield Neural Network.- 13. Application to Chaos Control and Chaos Synchronization.- References.- Index.