Problem of Mixed H2/H-Optimization

The problem of the robust optimal controller synthesis-mixed Н²/Н^∞-control problem is investigated. It is a two-criterion optimization problem. This controller combines advantages of Н^∞- and Н²-optimization theories. Two approaches to this type controller development are presented: solving three coupled matrix algebraic Riccati equations and reducing the Н²/Н^∞ -optimization problem for the state-feedback case to the problem of convex programming over the bounded set of real matrices. Several theorems, providing necessary and sufficient conditions to solve the mixed Н²/Н^∞-control problem, are considered.