The extended interactor in the study of nonregular control problems

Motivated by the problems arising in the study of the Morgan´s problems, the authors studied properties of the interactor of an extended system. The quasi-canonical Morse´s form, which serves as the basis upon which the extended system is defined, is introduced. This form is derived for a linear time-invariant right invertible system Σ(C, A, B) under the action of the classical feedback group extended by permutations of the outputs of the given system. The extended system has an invertible transform function whose interactor reveals all information about the infinite structure of Σ(C, A, B). This information plays a key role when a nonregular static state feedback is applied to the given system