Mixed H2/H∞ control:a convex optimization approach |
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Authors: | Khargonekar P.P. Rotea M.A. |
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Affiliation: | Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI; |
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Abstract: | The problem of finding an internally stabilizing controller that minimizes a mixed H2/H∞ performance measure subject to an inequality constraint on the H∞ norm of another closed-loop transfer function is considered. This problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint. Both the state-feedback and output-feedback problems are considered. It is shown that in the state-feedback case one can come arbitrarily close to the optimal (even over full information controllers) mixed H2/H∞ performance measure using constant gain state feedback. Moreover, the state-feedback problem can be converted into a convex optimization problem over a bounded subset of (n×n and n ×q, where n and q are, respectively, the state and input dimensions) real matrices. Using the central H∞ estimator, it is shown that the output feedback problem can be reduced to a state-feedback problem. In this case, the dimension of the resulting controller does not exceed the dimension of the generalized plant |
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