Control system analysis and design via the “second method” of lyapunov: I continuous-time systems

Abstract

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) controlsystem optimization; (d) design of relay servos. The discussion is essentially selfcontained, 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 stibject of a companion paper. © 1960 by ASME.