A new concept of strong controllability via the Schur complement for ARX models in adaptive tracking

We propose a new concept of strong controllability related to the Schur complement of a suitable limiting matrix. This new notion allows us to extend the previous convergence results associated with multidimensional ARX models in stochastic adaptive tracking. On the one hand, we carry out a sharp analysis of the almost sure convergence for both least squares and weighted least squares algorithms. On the other hand, we also provide a central limit theorem and a law of iterated logarithm for these two algorithms.