Fiedler line arizations for LTI state space systems and for rational eigenvalue problems

Abstract

The primary aim of this thesis is to develop a framework for direct methods for solutions of rational eigenvalue problems. To achieve this goal, we propose to reformulate the problem of solving a rational eigenvalue problem G( )u = 0 for 2 C and nonzero vector u 2 Cn to that of computation of transmission zeros and zero directions of a linear time invariant (LTI) system given by Ex (t) = Ax(t) + Bu(t) y(t) = Cx(t) + P( d dt )u(t) for which G( ) is the transfer function. Then the eigenvalues of G newline