Successive approximation for H∞

This paper gives three new algorithms for the H_∞ control problem based on the idea of successive approximation. Unlike the generally used solution procedure based on the central Riccati equation, the proposed algorithms use a gain-updating scheme which has the advantage of connecting any stabilizing gain to the H_∞ optimal gain. Various properties of the updating scheme are proved. In particular, it is shown under mild conditions that the existence, stabilizability and monotonicity of the solutions of the Riccati equation at each step are naturally guaranteed. The algorithms only involve an H_∞ norm evaluation problem at each step and are proved to be convergent to the central solution for the given parameter of H_∞ norm bound. These algorithms are particularly effective when the system order is large. A numerical example is given to illustrate the proposed algorithms.