Noninteracting control problem for structured transfer matrix systems

Abstract

The problem of determining a feedback controller which makes the closed-loop transfer matrix diagonal is known as the "noninteracting control problem" in system theory. Structured transfer matrix systems are linear systems given by transfer matrices of which the infinite zero order of each nonzero entry is known, while the associated infinite gains are unknown and assumed to be mutually independent. This paper derives necessary and sufficient conditions for the generic solvability of the noninteracting control problem for structured transfer matrix systems by dynamic output feedback. "Generic solvability" means solvability for almost all possible values for the infinite gains of the nonzero transfer matrix entries. The conditions are stated by generic essential orders, which are defined in terms of the minimal weight of the matchings in a bipartite graph associated with the structured transfer matrix systems.