Optimal l/sub ∞/ to l/sub ∞/ estimation for periodic systems

In this paper we consider the problem of finding a filter that minimizes the worst-case magnitude (l/sub /spl infin//) of the estimation error in the case of linear periodically time-varying systems subjected to unknown but magnitude-bounded (l/sub /spl infin//) 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 l/sub 1/-model matching problem subject to additional constraints. Taking advantage of the particular structure of the estimation problem, it is shown how standard methods of l/sub 1/ optimization, in particular the delay augmentation technique, can be suitably modified to solve this nonstandard problem.