The parameterization of MIMO systems in the open-loop balanced representation was introduced by Kabamba (1985) to show the advantages of using the balanced canonical form over other classical canonical forms as regards the guaranteed stability and minimality of the representation. The parameterization of MIMO systems in closed-loop balanced representation is introduced: the stability is guaranteed under particular conditions and the minimality is also assured. The importance that such a type of realization plays is fundamental in the synthesis of MIMO systems with assigned characteristic values; this allows us to investigate, for example, the stability of closed-loop systems with a low-order regulator. Indeed, for a defined class of MIMO systems, the introduced parameterization allows us to derive sufficient conditions for the closed-loop dissipativeness and for the stability of the reduced-order compensator, generalizing some results proved for S1SO systems.
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