Mixed H2/H∞ control via convex programming

In this paper we consider a mixed H₂/H_∞ control problem. This is 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. This problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint. We consider both state-feedback and output feedback problems. It is shown that in the state-feedback case one can come arbitrarily close to the optimal mixed H₂/H_∞ performance measure using a constant state-feedback gain. 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. Further, in this case, the dimension of the resulting controller does not exceed the dimension of the generalized plant. This conference paper is based on our recent paper [8] which contains complete details including proofs.