Rational stabilizing commutative controllers for unstable plant

The characteristic locus method provides a systematic way to extend the classical control design techniques to multivariable systems. In addition, the manipulation of the eigenfunctions of the open-loop transfer matrix also allows optimal control problems, usually formulated using H∞optimization theory, to be addressed in the same manner as for scalar systems, avoiding the difficulties in the choice of multivariable weights, a problem of multivariable H∞design. Furthermore, the relative stability margin objective can also be taken into account by maximizing the minimum distance of the characteristic loci of the open-loop transfer matrix to the critical point. In order to obtain optimal controllers, it is first necessary to guarantee the internal stability of the closed-loop system. In this paper, a complete characterization of the class of stabilizing commutative controllers for continuous-time systems is given and conditions for the existence of these controllers for unstable plants are presented.