Mixed H/sub 2//H/sub infinity / control: a convex optimization approach

The problem of finding an internally stabilizing controller that minimizes a mixed H/sub 2//H/sub infinity / performance measure subject to an inequality constraint on the H/sub infinity / 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 H/sub 2//H/sub infinity / 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/sub infinity / 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.>