  The usefulness of persistent excitation is well-known in the control
community. Thanks to a persistently excited adaptive tracking control, we show
that it is possible to avoid the strong controllability assumption recently
proposed in the multidimensional ARX framework. We establish the almost sure
convergence for both least squares and weighted least squares estimators of the
unknown parameters. A central limit theorem and a law of iterated logarithm are
also provided. All this asymptotical analysis is related to the Schur
complement of a suitable limiting matrix.
