Background
Gelig, Arkadii Khaimovich was born on October 12, 1931 in Leningrad, Russia. Son of Khaim Shaevich Gelig and Lidiya Dmitrievna Khudyakova.
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book
Stability and Oscillations of Nonlinear Pulse-Modulated Systems
(There are two main fields of application of pulse-modulat...)
There are two main fields of application of pulse-modulated sys tems, communications and control. Communication is not a subject of our concern in this book. Controlling by a pulse-modulated feed attracted our efforts. The peculiarity of this book is that all back the sampled-data systems are considered in continuous time, so no discrete time schemes are presented. And finally, we pay a little at tention to pulse-amplitude modulation which was treated in a vast number of publications. The primary fields of our interest are pulse width, pulse-frequency, and pulse-phase modulated control systems. The study of such systems meets with substantial difficulties. An engineer, who embarks on theoretical investigations of a pulse-mo dulated control, is often embarrassed by the sophisticated mathe matical tools he needs to know. When a mathematician, who looks for practical applications of his mathematical machinery, meets with these systems, he faces a lot of of complicated technical schemes and terms. Probably this is the reason why publications on pulse modu lation are seldom in scientific journals. As for books on this subject (save on amplitude modulation), the significant part of them is in Russian and hardly available for a non-Russian reader.
http://www.amazon.com/gp/product/1461272696/?tag=2022091-20
Stability and Oscillations of Nonlinear Pulse-Modulated Systems
(There are two main fields of application of pulse-modulat...)
There are two main fields of application of pulse-modulated sys tems, communications and control. Communication is not a subject of our concern in this book. Controlling by a pulse-modulated feed attracted our efforts. The peculiarity of this book is that all back the sampled-data systems are considered in continuous time, so no discrete time schemes are presented. And finally, we pay a little at tention to pulse-amplitude modulation which was treated in a vast number of publications. The primary fields of our interest are pulse width, pulse-frequency, and pulse-phase modulated control systems. The study of such systems meets with substantial difficulties. An engineer, who embarks on theoretical investigations of a pulse-mo dulated control, is often embarrassed by the sophisticated mathe matical tools he needs to know. When a mathematician, who looks for practical applications of his mathematical machinery, meets with these systems, he faces a lot of of complicated technical schemes and terms. Probably this is the reason why publications on pulse modu lation are seldom in scientific journals. As for books on this subject (save on amplitude modulation), the significant part of them is in Russian and hardly available for a non-Russian reader.
http://www.amazon.com/gp/product/081763987X/?tag=2022091-20
Stability of Stationary Sets in Control Systems With Discontinuous Nonlinearities (Series on Stability, Vibration and Control of Systems, Series a, Vol. 14)
(This book presents a development of the frequency-domain ...)
This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman Yakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines. Contents: Foundations of Theory of Differential Equations with Discontinuous Right-Hand Sides; Auxiliary Algebraic Statements on Solutions of Matrix Inequalities of a Special Type; Dichotomy and Stability of Nonlinear Systems with Multiple Equilibria; Stability of Equilibria Sets of Pendulum-Like Systems.
http://www.amazon.com/gp/product/9812387196/?tag=2022091-20
Arkadii Khaimovich Gelig
Edit ProfileEducation
Graduate mathematics, Leningrad State University, Russia, 1955. Doctor of Philosophy in Mathematics, Leningrad State University, Russia, 1961. Doctor of Science in Mathematics, Leningrad State University, Russia, 1985.
Career
Postgraduate Leningrad. Pedagogical Institute, Russia, 1955-1958. Engineer Metal Working Plant, Leningrad, Russia, 1958-1963.
Researcher Leningrad State University (now St. Petersburg State University), Russia, 1963-1990, head laboratory Russia, since 1991.
Achievements
Works
book
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Stability of Stationary Sets in Control Systems With Discontinuous Nonlinearities (Series on Stability, Vibration and Control of Systems, Series a, Vol. 14)
(This book presents a development of the frequency-domain ...)
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Stability and Oscillations of Nonlinear Pulse-Modulated Systems
(There are two main fields of application of pulse-modulat...)
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Stability and Oscillations of Nonlinear Pulse-Modulated Systems
(There are two main fields of application of pulse-modulat...)
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Stability of Stationary Sets in Control Systems With Discontinuous Nonlinearities (Series on Stability, Vibration and Control of Systems, Series a, Vol. 14)
Membership
Active St. Petersburg Brunch Memorial Society, since 2000. Member St. Petersburg Mathematics Society, St. Petersburg Society Informatics and Control.
Connections
Married Olga Ippolitovna Komarnitskaya (divorced 1971). Married Sophia Abramovna Rabkina, October 6, 1972. Children: Katherina, Vitalii.
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Born
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Nationality
Russian -
Ethnicity
Education
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1955
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1961
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1985
Career
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1955 - 1958
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1958 - 1963
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1963 - 1990