  In this paper we synthesize behavioral ideas with geometric control theory
and 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 systems (ODE-LTI). An algorithm for computing
an ODE-LTI that generates solutions of a given DAE-LTI is described. It is
shown that two different ODE-LTIs which represent the same DAE-LTI are feedback
equivalent. The proposed framework is then used to solve an LQ optimal control
problem for DAE-LTIs with rectangular matrices.
