Optimal l∞ to l∞ estimation for periodic systems

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 periodically time-varying systems subjected to unknown but magnitude-bounded (l_∞) inputs. These inputs consist of process and observation noises, and the optimization problem is considered over an infinite-time horizon. Lifting techniques are utilized to transform the problem to a time invariant l₁-model matching problem subject to additional constraints. Taking advantage of the particular structure of the estimation problem, it is shown how standard methods of l₁ optimization, in particular the delay augmentation technique, can be suitably modified to solve this nonstandard problem