Stability and Oscillations of Nonlinear Pulse-Modulated Systems

ISBN-13: 9781461272694 / Angielski / Miękka / 2012 / 362 str.

Arkadii Kh Gelig; Alexander N. Churilov

Opis

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.

Recenzje

"...A very comprehensive introduction...useful for researchers, professionals in control theory, and applied mathematics..."

--Simulation News Europe

Spis treści

1 Mathematical Description of Pulse-Modulated Systems.- 2 Stability of Equilibria. Miscellaneous Methods.- 3 Stability of Equilibria. Averaging Method.- 4 Stability of Processes. Averaging Method.- 5 Forced Periodic Oscillations. Method of Equations of Periods.- 6 Oscillations of PWM Systems. Fixed-Point Method.- 7 Oscillations of PFM Systems. Fixed-Point Method.- 8 Method of Harmonic Balance and Its Justification.- 9 Auto-Oscillations in Pulse Modulated Systems.- 10 Pulse-Width Modulated Systems of Phase Synchro¬nization.- A.1 Controllability, Observability, Nondegeneracy, Hurwitz.- Property.- A.2 Lyapunov Matrix Equation and Inertia Theorems...- A.3 Kalman—Yakubovich Lemma.- A.4 Auxiliary Statements Related to the Kalman—Yaku-bovich Lemma.- A.5 Estimates of a Functional.- A.6 Solvability of Matrix Inequalities (PWM Systems).- A.7 Solvability of Matrix Inequalities (PFM Systems).- A.8 Positive Kernels of Integral Equations.- A.9 Stability of Systems with Integral Quadratic Bounds.- A.10 Miscellaneous Statements.- References.