Mixed H2/H∞ control for continuous-time linear systems

The problem of mixed H₂/H_∞ control via state feedback for continuous-time systems is addressed. The plant is assumed linear time-invariant, but the results can be easily generalized to cope with uncertain systems in convex bounded domains. Two problems are solved: minimization of the H ₂-norm of a closed-loop transfer function under H _∞ constraints; and minimization of the H_∞-norm of a closed-loop transfer function under H₂ constraints. These two problems are transformed into equivalent convex problems by means of an appropriate parameter space choice. In both cases, if the constraint is relaxed, the control gain will assure an optimal norm level. Examples illustrate the theoretical results