Synthesis of fixed-architecture, robust H 2 and H ∞ controllers

This paper discusses and compares the synthesis of fixed-architecture controllers that guarantee either robust H 2 or H ∞ performance. The synthesis is accomplished by solving a Riccati equation feasibility problem resulting from mixed structured singular value theory with Popov multipliers. Whereas the algorithm for robust H 2 performance had been previously implemented, a major contribution described in this paper is the implementation of the much more complex algorithm for robust H ∞ performance. Both robust H 2 and H ∞ , controllers are designed for a benchmark problem and a comparison is made between the resulting controllers and control algorithms. It is found that the numerical algorithm for robust H ∞ performance is much more computationally intensive than that for robust H 2 performance. Both controllers are found to have smaller bandwidth, lower control authority and to be less conservative than controllers obtained using complex structured singular value synthesis.