MIXED H-2/H-INFINITY CONTROL - A CONVEX-OPTIMIZATION APPROACH

In this paper, we consider a mixed H-2/H-infinity control problem. This is the problem of finding an internally stabilizing controller that minimizes a mixed H-2/H-infinity performance measure subject to an inequality constraint on the H-infinity norm of another closed-loop transfer function. (This mixed H-2/H-infinity performance measure was called the "auxiliary cost" by Bernstein and Haddad, and is an upper bound on the H-2 norm of a transfer function.) This problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint. We consider both the state-feedback and output-feedback problems. It is shown that in the state-feedback case one can come arbitrarily close to the optimal (even over full information controllers) mixed H-2/H-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 x n and n x q, where n and q are, respectively, the state and input dimesions) real matrices. Using the central H-infinity estimator, it is shown that the output feedback problem can be reduced to a state-feedback problem. Further, in this case, the dimension of the resulting controller does not exceed the dimension of the generalized plant.