NEW DIRECTIONS OF RESEARCH IN NONLINEAR-SYSTEM THEORY

Recent developments in nonlinear system theory are surveyed. The survey is divided into three parts: the foundations of stability theory, the stability of large-scale systems, and differential-geometric methods. The author summarizes the research results in Lyapunov stability theory and input-output stability theory and comments on their relationship. Research findings in the area of stability of large-scale interconnected systems are presented, both from the Lyapunov and input-output viewpoints. Finally, the reader gets a glimpse of the still-developing area of differential-geometric methods for the analysis of nonlinear control systems. An easy-to-understand exposition of what differential-geometric methods have to offer concludes the survey. Several examples are given, and the references include several useful sources of additional information. 57 refs.