Persistency of excitation results for structured nonminimal models

It is frequently convenient to use specially structured nonminimal models for parameter estimation such as in the case of direct adaptive control where the model is parameterized in terms of the desired control law parameters. This is done, for example, in direct model reference adaptive control and in direct pole assignment adaptive control algorithms. It is shown that the parameters appearing in these nonminimal models can be uniquely estimated if and only if a certain design identity has a unique solution. The result is used to develop persistency of excitation results for these models