Constant McMillan Degree and the Continuous Stabilization of Families of Transfer Matrices

In indirect parameter adaptive control, one updates controller coefficients as new estimates of the plant are obtained. It is often of interest in that context to know if it is possible to design controllers that depend explicitly on plant parameters. For instance, if this dependence is polynomial or rational, the update itself consists simply of an evaluation, with no further computation. In addition to computational considerations, it is also of interest to know if one can design at least continuously on the parameters. From the work of Delchamps ([Del]), we know that indeed continuous, and even analytic, dependence of controllers on parameters is possible. In [Sol], combining ideas of Delchamps together with a result given in that reference, we showed that it is even possible to obtain rational or polynomial dependency. The basic assumption in this kind of result is always that the McMillan degree of the plant does not vary over the parameter space. As