THE BOUNDEDNESS, STABILITY AND REDUCIBILITY OF LINEAR HOMOGENEOUS SYSTEMS.
Abstract
Linear systems of first order differential equations dX/dt = A(t)X, X(t sub 0) = C is considered, where C is a square, non-singular, constant matrix and A(t) is a square matrix of complex valued functions of the real argument t defined over some interval containing t sub 0. Three interdependent questions concerning these equations are discussed: (1) the boundedness of the matrix integral X(t), (2) the stability of the system, and (3) the exchange of the system for an equivalent system possessing a constant coefficient matrix. With regard to the last consideration, often called 'reducibility', four propositions by the Soviet mathematician V. A. Yakabovic are introduced. These results appear to be significant generalizations of the Lyapunov criterion concerning the reducibility of linear systems possessing periodic coefficient matrices. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1965
- Accession Number
- AD0617306
Entities
People
- Max Robert Lund
Organizations
- University of Utah