The generation of adaptive law structures for globally convergent adaptive observers

Observing the state of an unknown linear system by means of a parametrized representation of the standard Luenberger observer with an additional adaptive loop (adaptive observer) is considered. A general technique on how to construct suitable adaptive laws for this additional loop is presented and it is proven that these adaptive laws always result in global and arbitrarily fast convergence of the adaptive process. Because the adaptive laws can assume a variety of different structures, both structural and parametric degrees of freedom in the adaptive law (rather than the so far available parametric degrees alone) are obtained, which can be used in a future optimization of the adaptive observer performance.