INFINITE EIGENVALUE METHOD FOR STABILITY ANALYSES OF CANONICAL LINEAR-SYSTEMS WITH PERIODIC COEFFICIENTS

This paper presents a technique that provides both necessary and sufficient conditions for stability of canonical linear differential equations with periodic coefficients and is well-suited for numerical application. Existing methods of stability analyses, not subject to small parameter restrictions, such as the widely used Floquet Numerical Integration Method (FNIM) and the Infinite Determinant Methods provide necessary conditions but are impractical for providing sufficient conditions for this class of systems with multiple degrees of freedom. Furthermore, the Infinite Determinant Methods are restricted to only certain classes of linear periodic systems whereas the FNIM is subject to numerical problems when dealing with canonical systems. The method proposed in this paper, referred to as the Infinite Eigenvalue Method (IEM), is based on Floquet theory and the Infinite Determinant Methods. It is applicable to the general class of multiple degree of freedom linear canonical systems and is not subject to small parameter restrictions. A brief review of Floquet theory and the FNIM is given. The IEM is then presented and applied to a spacecraft dynamics problem of current interest. The FNIM is applied to the same problem and the two methods are compared. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.