On Structural Invariants and the Root-Loci of Linear Multi-Variable Systems

The geometric nature of the infinite zeros of the root-loci of linear multi-variable 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