On poles and zeros of linear systems

The problem of determining the poles and zeros of a linear system is considered. Also pointed out is that this problem is mathematically equivalent to the generalized eigenvalue problem of the form
\lambda Ax =Bx
, which may be solved by means of some wellestablished numerical techniques. Two practical and reliable algorithms are presented. The first algorithm is more general than the second and can be effectively used to obtain the poles and zeros of a linear system even without knowing its state-space representation. The second algorithm assumes that the state-space equations of the system are known and takes full advantage of their special form. Both algorithms also offer considerable savings in computational effort when applied to multiple-input multiple-output systems. Several examples which illustrate the proposed methods and their computational characteristics are included.