Adaptive control of multivariable systems with reduced prior knowledge

We show that it is possible to globally and adaptively stabilize linear multivariable systems with reduced prior knowledge of the high frequency gain. In particular, we relax the restrictive (non-generic) symmetry condition usually required to solve this problem. Instrumental for the establishment of our result is the use of the new immersion and invariance approach to adaptive control recently proposed in the literature. The controllers obtained with this technique are not certainty equivalent, though smooth and without projections, and the resulting Lyapunov functions contain cross-terms between the plant states and parameter errors.