STATE-SPACE REALIZATIONS OF LINEAR DIFFERENTIAL-ALGEBRAIC-EQUATION SYSTEMS WITH CONTROL-DEPENDENT STATE-SPACE

This note addresses the derivation of state-space realizations for the feedback control of linear, high-index differential-algebraic-equatio n systems that are not controllable at infinity. In particular, a clas s of systems is considered for which the underlying algebraic constrai nts involve the control inputs, and thus a state-space realization can not be derived independently of the feedback controller. The proposed methodology involves the design of a dynamic state feedback compensato r such that the underlying algebraic constraints in the resulting modi fied system are independent of the new inputs. A state-space realizati on of the feedback-modified system is then derived that can be used as the basis for controller synthesis.