Stabilizability of Second Order Bilinear Systems,
Abstract
This report concerns the stabilizability of second order bilinear systems. While a large literature devoted to the structural properties of such systems has developed over the past decade, it is fair to say that little is understood regarding the qualitative behavior of trajectories. Recently, several authors have investigated the stabilizability of systems. These papers derive sufficient conditions and construct controllers to stabilize systems which meet specific and quite restrictive requirements. A constant pure quadratic feedback law is shown to stabilize. It is demonstrated that a constant linear and quadratic feedback law forces trajectories into an arbitrarily small bounded neighborhood of the origin. It is our opinion that a significant understanding of bilinear systems will not be possible until more systematic analysis has been accomplished. Accordingly, in this report we concentrate on a simple problem in some detail. Specifically, we give necessary and sufficient conditions for the existence of a constant linear feedback controller to stabilize. Even given the limited sccope of this problem, it is safe to say that the statement of necessary and sufficient conditions is possible only because of recent results in the stability of quadratic systems developed by the authors.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1981
- Accession Number
- ADA111073
Entities
People
- Daniel E. Koditschek
- Kumpati S. Narendra
Organizations
- Yale University