Optimal l∞ to l∞ estimation

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 which stem from the resulting l^∞-induced norm minimization problem.