  This thesis applies Floquet theory to analyze linear periodic time-varying
(LPTV) systems, represented by a system of ordinary differential equations
(ODEs) that depend on a time variable t and have a matrix of coefficients with
period T>0. The transition matrix of an LPTV system represented by a square
periodic-function matrix A(t)=A(t+T) can be expressed as the product of a
square periodic function matrix P(t)=P(t+T) and an exponentiated square matrix
of the form Rt, where R is a constant matrix (independent of t). Despite the
validity of Floquet theory, it is difficult to find an analytical closed form
for the matrices P(t) and R when the transition matrix {\Phi}_A (t,t_0 ) is
unknown. In essence, it is difficult to find an analytical solution for an LPTV
system (i.e., a closed form for its transition matrix). The research results
show that for a given family of periodic matrices A(t), we can compare the
powers of {\omega} that multiply the harmonics (i.e., {\omega} is part of the
coefficients multiplying the cosine [sine] factors in even [odd]
representations or of the exponential factors in complex representations) to
determine the matrices P(t) and R. In addition, the results lead to relations
between LPTV systems at frequency {\omega} and the associated linear
time-invariant system, which is defined by having zero frequency ({\omega}=0).
