Mixed H2/ESPR (extended strictly positive real) control for state-feedback case

This paper considers a mixed H₂/ESPR control problem for the state-feedback case. The problem is to find an internally stabilizing controller that minimizes a mixed H₂/ESPR performance measure subject to an inequality constraint on the ESPRness (extended strictly positive real) 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. It is shown that the state-feedback problem can be converted into a convex optimization problem over a bounded set of matrices, and that in the state-feedback problem, one can come arbitrary close to the optimal (even over full information controllers) mixed H₂/ESPR performance measure using constant gain state-feedback