On the Solution of the Boundary Value Problem of First Order Lyapunov System of Differential Equations

Abstract: In this paper, we present results on the existence and uniqueness of a solution to the first order non-homogeneous Lyapunov system of differential equations satisfying general two-point boundary conditions. A variation of parameters type of formula is derived to construct an integral form of the solution. The uniqueness of the solution is established through the least squares solution of a double-sided matrix equation associated with the boundary value problem.