Boundary recursion for descriptor variable systems

It is shown that if an n-dimensional descriptor variable system satisfies the properties of solvability and controllability, the family of solutions is n-dimensional and the set of two-point boundary values that are consistent with the system can be expressed as the solutions to a linear system of equations involving only the boundary values. This equation is termed a boundary mapping equation and it provides a compact representation of the system. The boundary mapping generalizes the state-transition matrix associated with state variable systems. The author presents the boundary mapping theory, describes the recursive processes required, and applies both to some special cases, including general linear time-invariant systems and adjoint systems.>