Infinite eigenvalue assignment for singular systems (Q5953710)

The infinite eigenvalue assignment problem for singular systems described by NEWLINE\[NEWLINEE\dot x= Ax+ Bu,\quad E, A\in\mathbb{R}^{n\times n},\quad B\in\mathbb{R}^{n\times m},\quad \text{det }E= 0\tag{1}NEWLINE\]NEWLINE is studied.NEWLINENEWLINENEWLINENecessary and sufficient conditions are established for the existence of a state feedback for (1) such that the closed-loop system is regular and has only infinite eigenvalues.NEWLINENEWLINENEWLINENumerical algorithms based on an orthogonal reduction to an upper Hessenberg form are given and illustrated by three examples.