On achievable bisimulations for linear time-invariant systems

We consider here the problem of finding a controller for a system such that when interconnected to the plant, we get a system which is bisimilar to the desired system. We give necessary and sufficient conditions for the existence of such a controller. The systems we consider are ordinary linear time invariant dynamical systems described by state space equations. We briefly compare our results with similar results in the behavioral approach to systems´ theory. The advantage of using the notion of bisimilarity is that it applies to state space systems and the computations involved are operations on real matrices.