Immersion and invariance adaptive control of linear multivariable systems

We show in this paper that it is possible to globally adaptively stabilize linear multivariable systems with reduced prior knowledge of the high-frequency gain. In particular, we relax the restrictive (nongeneric) 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 or overparameterizations—and the resulting Lyapunov functions contain cross-terms between the plant states and the parameter errors.