On structural invariants and the root-loci of linear multivariable systems

Abstract

The geometric nature of the infinite zeros of the root-loci of linear multivariate systems is investigated using the canonical form derived by Morse (1973). It is shown that an invertible system S(A, B, C) has integer-order infinite zeros in the generic case equal to the controllability indices of a pair (A + KC, B), that suitable choice of proportional output feedback guarantees the absence of other than integer-order zeros and that the orders and asymptotic directions of the infinite zeros are independent of constant state feedback and output injection.