Duality and basis functions for robust H2-performance analysis

The robust H2-Performance of a plant with a prescribed uncertain component refers to its white noise rejection level in the worst case (with respect to its uncertainty set). In this paper, we derive a dual formulation for the computation of the robust H2-performance of a plant with unit gain structured uncertainty. The dual framework gives a tight lower bound on robust H2-Performance with no duality gap with respect to the primal approach (Paganini, 1995a). We also show how the upper and lower bounds for the robust H2-Performance of a plant may be computed using semidefinite programming/linear matrix inequality-type formulae based on basis functions, and provide an example which enables us to demonstrate the relative merits and the complementary nature of the basis function and the gridding approaches to robust H2-performance analysis, for both the primal and the dual formulations.

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