Decoupling with Stability of Linear Multivariable Systems: an Algebraic Approach

The result that a linear multiapproach, and the solution is expressed in terms of variable system is decouplable with stability the infinite and unstable contents of the system. The if and only if its associated stable interactor decoupling problem with stability of nonsquare sysis diagonal, is proved in this paper using an tems is considered in (Ruiz-León et al., 1995) using algebraic approach. As it will be shown, this a polynomial equation approach, and a solution to condition is actually equivalent to the coincithis problem is reported. However, the necessary dence between the infinite and unstable global and su cient conditions presented in this reference structure (infinite and unstable zeros) and the to solve the problem are implicit in the sense that the row infinite and unstable structure of the sysexistence of a solution is stated in terms of the existem. Two procedures are presented to comtence of a biproper and bistable rational matrix with pute a state feedback which decouples the syscertain properties, thus restricting a great deal the tem with stability, the first one based on the applicability of this result. Nevertheless, when these solution of a polynomial matrix equation, and conditions are particularized to the case of square the second one based on the static left kernel systems, a solution can be obtained in terms of the of a strictly proper rational matrix. Illustradiagonality of the stable interactor of the system. tive examples are also presented. In this paper, using an algebraic approach, it is proved that the decoupling problem with stability Keywords— Linear systems, Decouhas a solution if and only if the stable interactor pling, Stability, Infinite structure, Algebraic of the system is a diagonal matrix. An important approach. result, shown in our development, is the fact that the action of a state feedback on a stable system which preserves internal stability can be represented