State Space Formulas for Transfer Poles at Infinity

摘要

Formulas for the transfer pole/zero structure at infinity of linear timeinvariant systems are given in terms of subspaces of the input and output spaces. A characterization of the existence of a transfer function as well as its left/right invertibility is given by using the same subspaces. For systems that are represented in descriptor form the formulas are given in terms of the matrices E, A, B, C and D. No specific assumptions are made on the descriptor representation; in particular, the matrices E and A may be nonsquare. As easy corollaries, known formulas are recovered for the zeros at infinity of standard state space representations and for the infinite elementary divisors of matrix