Robust H∞ Filter Design Using Frequency Gridding

This paper considers the design of robust H∞ filters for continuous-time linear systems with uncertainties described by integral quadratic constraints (IQCs). The synthesis problem can be converted into an infinite-dimensional optimization with frequency dependent linear matrix inequality constraints on the filter and IQC multipliers. This optimization is approximated by a finite dimensional semidefinite program by restricting the filter to be a linear combination of basis functions and enforcing the constraints on a finite, but dense, grid of frequencies. A heuristic algorithm is described to quickly solve the resulting finite dimensional optimization. A small example is provided to demonstrate the proposed algorithm.