Decoupling with stability of linear multivariable systems: An algebraic approach

Abstract

The result that a linear multi-variable system is decouplable with stability if and only if its associated stable interactor is diagonal, is proved in this paper using an algebraic approach. As it will be shown, this condition is actually equivalent to the coincidence between the infinite and unstable global structure (infinite and unstable zeros) and the row infinite and unstable structure of the system. Two procedures are presented to compute a state feedback which decouples the system with stability, the first one based on the solution of a polynomial matrix equation, and the second one based on the static left kernel of a strictly proper rational matrix. Illustrative examples are also presented.