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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.