Optimal, worst case filter design via convex optimization

We propose a convex optimization method for optimal robust linear filter design. This is based on the observation that the design problem, which is infinite dimensional, is convex in the filter. It is shown that finite dimensional relaxations can be used to get arbitrary close to the optimal solution. The design procedure constitutes successive finite dimensional approximations, involving worst case analysis to get converging upper and lower bounds. Our approach differs from standard robust filtering techniques. Usually, these minimize a specific choice of upper bound of the . The choice is usually well-motivated, but partially made for computational simplicity. The computational demands put forth in this paper are much larger.