On Simultaneous H2-Optimization of Several Performance Bounds

Simultaneous optimisation of several criteria is an important and interesting subject. Even the standard H2-case is non-trivial. The problem is here treated for the general MIMO case for two conflicting objectives (the results directly generalise to several performance measures). A seminorm D2 is introduced to describe the situation. The state-space solution technique in [Khargonekar and Rotea, 1991] is simplified and generalized slightly. It is shown that the method simplifies when the controller is SISO, SIMO or MISO. A polynomial method is also given, together with an example that illustrates the results.