On Control Systems Described by a Class of Linear Differential-Algebraic Equations: State Realizations and Linear Quadratic Optimal Control

Control systems described in terms of a class of linear differential-algebraic equations are introduced. Under appropriate relative degree assumptions, a procedure for obtainig an equivalent state realization is developed using a singular value decomposition. Properties such as stability, controllability, observability, etc. for the differential algebraic system may be studied directly from the state realization. An optimal linear quadratic problem for the differential-algebraic system is aiso studied and results are obtained using the derived state realization. This approach to control of this class of differential-algebraic equations, using a transformation to obtain a state realization, completely avoids the need for any new control theoretic machinery.