Accession Number : AD0617306

Title :   THE BOUNDEDNESS, STABILITY AND REDUCIBILITY OF LINEAR HOMOGENEOUS SYSTEMS.

Descriptive Note : Master's thesis,

Corporate Author : UTAH UNIV SALT LAKE CITY

Personal Author(s) : Lund,Max Robert

Report Date : JUN 1965

Pagination or Media Count : 46

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)

Descriptors :   (*DIFFERENTIAL EQUATIONS, LINEAR SYSTEMS), MATRICES(MATHEMATICS), STABILITY, COMPLEX VARIABLES

Distribution Statement : APPROVED FOR PUBLIC RELEASE