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This book presents the recently introduced and already widely referred semi-discretization method for the stability analysis of delayed dynamical systems. Delay differential equations often come up in different fields of engineering, like feedback control systems, machine tool vibrations, balancing/stabilization with reflex delay. The behavior of such systems is often counter-intuitive and closed form analytical formulas can rarely be given even for the linear stability conditions. If parametric excitation is coupled with the delay effect, then the governing equation is a delay differential equation with time periodic coefficients, and the stability properties are even more intriguing. The semi-discretization method is a simple but efficient method that is based on the discretization with respect to the delayed term and the periodic coefficients only. The method can effectively be used to construct stability diagrams in the space of system parameters.
List of contents
Introducing delay.- Basic delay differential equations.- Newtonian examples.- Engineering applications.- Summary.- References.
About the author
Gabor Stepan is a Professor in the Department of Applied Mechanics at the Budapest University of Technology and Economics.
Summary
This book presents the recently introduced and already widely referred semi-discretization method for the stability analysis of delayed dynamical systems. Delay differential equations often come up in different fields of engineering, like feedback control systems, machine tool vibrations, balancing/stabilization with reflex delay. The behavior of such systems is often counter-intuitive and closed form analytical formulas can rarely be given even for the linear stability conditions. If parametric excitation is coupled with the delay effect, then the governing equation is a delay differential equation with time periodic coefficients, and the stability properties are even more intriguing. The semi-discretization method is a simple but efficient method that is based on the discretization with respect to the delayed term and the periodic coefficients only. The method can effectively be used to construct stability diagrams in the space of system parameters.
Report
From the reviews:
"The goal of this book is to present the semi-discretization method for the stability analysis of linear periodic delay systems. ... The book is very well written and organized. ... is very interesting from both theoretical and applied points of view. ... a good list of references to the relevant literature is included. It is a good source to introduce Ph.D. students to the subject, and also a useful reference book for researchers in many areas where time-delay systems play an important role ... ." (Eduardo Liz, Mathematical Reviews, Issue 2012 f)
"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 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." (Tadeusz Kaczorek, Zentralblatt MATH, Vol. 1245, 2012)
