Originally published as volume 5 in the series: Mathematics and its Applications
2nd ed. 2008
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Answers a question that has not been solved in more than 60 years: what is sufficient and necessary condition for the absolute stability of the Lurie problem?
Includes new ideas and methodology that can be generalized to solve stability problems of other types of nonlinear systems
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.
Principal Theorems on Global Stability.- Sufficient Conditions of Absolute Stability: Classical Methods.- Necessary and Sufficient Conditions for Absolute Stability.- Special Lurie-Type Control Systems.- Nonautonomous Systems.- Systems with Multiple Nonlinear Feedback Controls.- Robust Absolute Stability of Interval Control Systems.- Discrete Control Systems.- Time-Delayed and Neutral Lurie Control Systems.- Control Systems Described by Functional Differential Equations.- Absolute Stability of Hopfield Neural Network.- Application to Chaos Control and Chaos Synchronization.