Output Feedback in Descriptor Systems

A summary is given of conditions under which a descriptor, or generalized state-space, system can be regularized by output feedback. Theorems are presented showing that under these conditions proportional and derivative output feedback controls can be constructed such that the closed loop system is regular and has index at most one. This property ensures the solvability of the resulting system of dynamic-algebraic equations. A canonical form is given that allows the system properties as well as the feedback to be determined. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way. A computational algorithm for improving the ‘conditioning’ of the regularized closed loop system is described.

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