Internal stabilization and decoupling in linear multivariable systems by unity output feedback compensation

We consider the problem of internally stabilizing and simultaneously diagonaly decoupling a linear multivariable system by unity output feedback compensation. A sufficient condition is derived for the existence of a compensator C(s) such that when employed in a unity feedback loop involving the proper transfer function matrix Po(s) of a free of unstable hidden modes system Σ(Po), will not only internally stabilize the feedback closed loop system Σ(Po, C) but will also give rise to a closed loop transfer function matrix Hdiag yr, which is non-singular, diagonal and has desired poles. Based on this analysis an algorithmic procedure for the computation of such a compensator is presented.