Introduction to the Theory of Stability

. Texts in Applied Mathematics Springer-Verlag, New York, Third edition, (1997)


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.

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