Mixed H2 and H∞ control

Mixed H₂ and H_∞ norm analysis and synthesis problems are considered in this paper. It is shown that the mixed norm analysis combined with structured uncertainty can be used to give bounds on robust H₂ and H_∞ performance. It is also shown that the mixed norm controller shares a separation property similar to those of pure H₂ or H_∞ controllers. The obvious advantage for a mixed norm is that it gives a natural trade-off between H₂ performance and H_∞ performance, and provides a potential framework for extending the μ-synthesis framework to address robust H₂ performance. A simple example is used to motivate the possible advantages such a framework might have over a pure H_∞ theory.