Mixed H_2 and H∞ performance objectives. II. Optimal control

This paper considers the analysis and synthesis of control systems subject to two types of disturbance signals: white signals and signals with bounded power. The resulting control problem involves minimizing a mixed H_2 and H∞ norm of the system. It is shown that the controller shares a separation property similar to those of pure H_2 or H∞ controllers. Necessary conditions and sufficient conditions are obtained for the existence of a solution to the mixed problem. Explicit state-space formulas are also given for the optimal controller.