COMPUTATION OF STATE REALIZATIONS FOR CONTROL-SYSTEMS DESCRIBED BY A CLASS OF LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS

Control systems described in terms of a class of linear differential-algebraic equations are introduced. Under appropriate relative degree assumptions, a computational procedure for obtaining 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. For linear constrained hamiltonian systems, it is shown that the procedure provides a state realization in which the hamiltonian structure is preserved. Similar results are obtained for constrained gradient systems. Control of systems described by this class of differential-algebraic equations, using a transformation to obtain a state realization, completely avoids the need for any new control theoretic machinery.