On the adaptive stabilization of linear systems (Q1820743)

This paper establishes the equivalence of the adaptive stabilization problem for a finite family of linear systems to the algebraic problem of uniform (simultaneous) stabilization. It is shown that for a finite family of linear systems whose output measurements are corrupted by white Gaussian noise to be adaptively stabilizable by a feedback matrix, it is necessary and sufficient that the same family of systems is simultaneously output stabilizable by the same feedback matrix.