On optimal ℓ^∞ to ℓ^∞ filtering

In this paper we consider the problem of finding a filter that minimizes the worst case magnitude (ℓ^∞) of the estimation error in the case of linear time-invariant systems subjected to unknown but magnitude-bounded (ℓ^∞) inputs. These inputs consist of process and observation noise, as well as initial conditions; also, the optimization problem is considered over an infinite time horizon. Taking a model matching approach, suboptimal solutions are presented that stem from the resulting ℓ^∞-induced norm-minimization problem.