Optimal control with mixed H_2 and H∞ performance objectives

Abstract

This paper considers the analysis and synthesis of control systems subject to two types of disturbance signals: signals with bounded power spectral density 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 pare H_2 or H∞. controller. It is also shown that the mixed problem reduces naturally to H_2 and H∞ problem in special cases. Some necessary and sufficient conditions are obtained for the existence of a solution to the mixed problem. Explicit state space formulae are given for the optimal controllers.