State representations of linear systems with output constraints

We derive state space representations for linear systems that are described by input/state/output equations and that are subjected to a number of constant linear constraints on the outputs. In the case of a general linear system, the state representation of the constrained system is shown to be essentially nonunique. For linear Hamiltonian systems satisfying a nondegeneracy condition, there is a natural and unique choice of the representation which preserves the Hamiltonian structure. In the linear systems setting we give an algebraic proof that a system withn degrees of freedom underk constraints becomes a system withn−k degree of freedom. Similar results are obtained for linear gradient systems.