Geometric Conditions for Generic Structure of Multivariable Root-Loci

摘要

Using the properties of the inverse (A-pBC)-1 the asymptotic directions of the infinite zeros of the multivariable root-locus of a multivariable feedback system S(A,B,C) are characterized by constrained eigenvalue problems. Generic conditions for the existence of only integer order infinite zeros are identified in terms of subspaces in the (A,B) invariance algorithm and its dual. Major assumptions in the analysis are that the system is invertible with no pole or zeros at the origin of the complex plane. Origin shift techniques indicate that there is no real loss of generality.