This book presents a modern and self-contained treatment of the Liapunov
method for stability analysis, in the framework of mathematical
nonlinear control theory. A Particular focus is on the problem of the
existence of Liapunov functions (converse Liapunov theorems) and their
regularity, whose interest is especially motivated by applications to
automatic control. Many recent results in this area have been collected
and presented in a systematic way. Some of them are given in extended,
unified versions and with new, simpler proofs. In the 2nd
edition of this successful book several new sections were added and old
sections have been improved, e.g., about the Zubovs method, Liapunov
functions for discontinuous systems and cascaded systems. Many new
examples, explanations and figures were added making this book
accessible and well readable for engineers as well as mathematicians.