Infinite eigenvalue assignment for singular systems Original Research Article

In this paper, the infinite eigenvalue assignment problem for singular systems is studied. Necessary and sufficient conditions are presented under which there exists a state feedback such that the closed-loop system is regular and has only infinite eigenvalues. The main result is proved constructively based on some simple numerical algorithms. These numerical algorithms consist of an orthogonal reduction to an upper (block) Hessenberg form and a simple linear recursion deduced from 2×2 Givens transformations.