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.
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.
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