Nonlinear System Analysis and Synthesis. Part I. Study of Lyapunov Functions for Problems of Control and of Optimality of Linear Systems

摘要

Research covered in this report may be broken into four parts. I. Lyapunov Function for the Problem of Lur'e in Automatic Control. This problem is completely resolved by giving conditions for the existence of a Lyapunov function and an algorithm for its construction. II. On Polynomial Lyapunov Function. A preliminary study of the use of polynomial Lyapunov functions in the study of stability, with particular attention to possible computational utilization. III. When is a Linear Control System Optimal. Discussion of the problem: Given a control law, for what performance indices is it optimal. This treatment involves the use of frequency domain techniques. IV. ASP Modifications. A description of changes and proposed changes in the ASP Program. This program is more completely described in ASD-TR-61-27, Volume I and II. (Author)