Linear optimal algorithms in set membership identification

In this paper we investigate the optimality properties of linear identification algorithms. In particular, we study set membership identification problems, in which the output is linear in the parameters and it is corrupted by additive noise. The optimality properties of least squares algorithm are investigated in the case of bounded amplitude noise when the norms used in the parameter space are different from inner product norms. When the parameter space is l_∞ normed and the output space is l_∞ or l₁ normed, it is shown that linear optimal algorithms exist and can be computed by solving linear programming problems