Partial Eigenvalue Assignment in Continuous-Time Descriptor Systems Via Derivative State Feedback

Abstract

A method for stability of the descriptor continuous-time linear system is focused. For easily, it is converted to a standard continuous-time linear system by the definition of a derivative state feedback. Then partial eigenvalue assignment is used for obtaining state feedback and showing stability and controllability of the standard system. In partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear systems are reassigned, while leaving the rest of the spectrum invariant and for reassigning, similarity transformation is used. Using partial eigenvalue assignment is easier than using eigenvalue assignment. Because by partial eigenvalue assignment, size of matrices and state and input vectors are decreased and stability is kept, too. Also concluding remarks and an algorithm are proposed to the descriptions be obvious. At the end, convergence of state and input vectors in the descriptor system to balance point (zero) are showed by figures in numerical examples.