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Semi-discretization for time-delay systems. Stability and engineering applications. (English) Zbl 1245.93004

Applied Mathematical Sciences 178. New York, NY: Springer (ISBN 978-1-4614-0334-0/hbk). x, 174 p. (2011).
This monograph presents a numerical technique, called the semi-discretization method, for the stability analysis of linear time-periodic and time-delay systems. Partial differential equations describing the systems are discretized only along the spatial coordinates while the time coordinate is unchanged. The book is based mostly on the author’s research work over the last 10 years.
The book consists of five chapters, appendix and references. Chapter 1 gives short introduction to linear time-delay systems theory. Chapter 2 is devoted to the construction of the stability charts for some delay-differential equations. Chapter 3 deals with the semi-discretization higher-order methods and discusses numerical issues. The semi-discretization method is applied in Chapter 4 to some systems with different delay types. Chapter 5 is devoted to real-world mechanical engineering applications such as varying spindle speed turning, stability of milling processes, periodic control systems with feedback delay and parametric excitation of balancing. ln Appendix, the solution to linear ordinary differential equations, the Routh-Hurwitz criterion and some Matlab codes are re-called.
The book is addressed to graduate and PhD students as well to scientists working in the field of mechanical, electrical and chemical engineering, control theory biomechanics etc.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93C55 Discrete-time control/observation systems
93C95 Application models in control theory

Software:

Matlab; DDE-BIFTOOL
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