Solutions of differential-algebraic equations as outputs of LTI systems: Application to LQ control problems

In this paper we propose a unified geometric framework for representing all solutions of a Linear Time Invariant Differential-Algebraic Equation (DAE-LTI) as outputs of classical Linear Time Invariant Ordinary Differential Equations (ODE-LTI). The proposed framework is then used to solve an LQ optimal control problem for DAE-LTIs with rectangular matrices.