Book,
Introduction to the Theory of Stability
Texts in Applied Mathematics Springer-Verlag, New York, Third edition, (1997)
Abstract
This book concerns itself with the theory of stability
of motion in dynamic systems with respect to variation
of the initial conditions of the motion. The theories
of stability developed by Lagrange, Liapunov, Chetaev,
Krasovsky, Thomson and Tait, Hurwitz, Nyquist and new
results obtained by the author are presented. Chapter
headings include: formulation of the problem; the
direct Liapunov method --- autonomous systems;
stability of equilibrium states and stationary motions
of conservative systems; stability in the first
approximation; stability of linear autonomous systems;
the effect of force type on stability of motion; the
stability of non-autonomous systems; application of
the direct method of Liapunov to the investigation of
automatic control systems, and the frequency method of
stability analysis.
