Stability and Oscillations of Nonlinear Pulse-Modulated Systems Arkadii Kh. Gelig, Alexander N. Churilov Birkhauser (1998), price $98.00, ISBN: 081763987X.
Reviewer: Alois Steindl, Institute for Mechanics, Vienna University of Technology.

The book deals with a class of systems, where different kinds of discontinuous input functions are applied to partial or ordinary differential equations. These input functions, which can be generated by feedback controllers, will often be piecewise continuous functions in time, with the switching instances triggered by the state of the system.

The book covers so-called "pulse-width modulation", "pulse-phase modulation", "pulse-amplitude modulation" and "integral pulse-width modulation". It treats the stability of steady solutions for asymptotically stable continuous linear parts (CLP) and for CLPs with one neutral eigenvalue. Also the existence and stability of forced periodic and "auto-oscillative" motions are investigated.

For the mathematical investigation different methods are used and presented, for example the "direct Lyapunov method", averaging, "equations of periods", fixed point method, and harmonic balance. All of these methods are described and applied to different problem settings.

In my opinion this book fulfills two tasks: As a reference book it helps the engineers and mathematicians to classify, design and investigate control systems in real world applications. And it introduces the mathematicians, who want to deal with various kinds of feedback control systems, to the technical terms in a demanding field of applications.