LMI based design of mixed H2/H∞ controllers: the state feedback case

A mixed H₂/H_∞ controller minimizes the H₂ norm of a closed-loop map over all admissible controllers while satisfying an H_∞ constraint on another closed-loop map. In the paper we develop an efficient iterative algorithm for numerical computation of the fixed-order mixed controllers. In the proposed technique we break up the original non-convex problem into a series of convex subproblems each of which can be converted into semidefinite programming problems that can be easily solved. Numerical examples are presented to demonstrate the improvement in the H₂ performance of the mixed H₂/H_∞ controller over the commonly used central H_∞ controller