The groundbreaking work of Russian mathematician A. M. Liapunov (1857-1918) on the stability of dynamical systems was overlooked for decades because of political turmoil. During the Cold War, when it was discovered that his method was applicable to the stability of aerospace guidance systems, interest in his research was rekindled. It has remained high ever since.
This monograph on both the theory and applications of Liapunov's direct method reflects the work of a period when the theory had been studied seriously for some time and reached a degree of completeness and sophistication. It remains of interest to applied mathematicians in many areas. Topics include applications of the stability theorems to concrete problems, the converse of the main theorems, Liapunov functions with certain properties of rate of change, the sensitivity of the stability behavior to perturbations, the critical cases, and generalizations of the concept of stability.

Preface to the English Edition
Preface to the German Edition
Fundamental Concepts
Sufficient Conditions for Stability or Instability of the Equilibrium
Applications of the Stability Theorems to Concrete Problems
The Converse of the Main Theorems
Liapunov Functions with Certain Properties of Rate of Change
The Sensitivity of the Stability Behavior to Perturbations
The Critical Cases
Generalizations of the Concept of Stability
Bibliography
Author Index
Subject Index