Control System Analysis and Design Via the “Second Method” of Lyapunov: I—Continuous-Time Systems

[+] Author and Article Information
R. E. Kalman

Research Institute for Advanced Study, Baltimore, Md.

J. E. Bertram

IBM Research Center, Yorktown Heights, N. Y.

J. Basic Eng 82(2), 371-393 (Jun 01, 1960) (23 pages) doi:10.1115/1.3662604 History: Received August 10, 1959; Online November 04, 2011


The “second method” of Lyapunov is the most general approach currently in the theory of stability of dynamic systems. After a rigorous exposition of the fundamental concepts of this theory, applications are made to (a) stability of linear stationary, linear nonstationary, and nonlinear systems; (b)estimation of transient behavior; (c) control-system optimization; (d) design of relay servos. The discussion is essentially self-contained, with emphasis on the thorough development of the principal ideas and mathematical tools. Only systems governed by differential equations are treated here. Systems governed by difference equations are the subject of a companion paper.

Copyright © 1960 by ASME
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