Exact and Approximate Solutions to a Class of Multiobjective Controller Synthesis Problems

In this paper, we consider a multiple objective control problem. If the exogenous input matrices in a state-space model of the plant under control satisfy a generic rank condition, we show that all the individual state-feedback controllers which achieve desirable performance and robustness levels (as measured by suitable closed loop transfer matrices) can be combined to generate a single state-feedback controller that simultaneously achieves the same performance and robustness levels. In the output feed-back case we show how to recover (to any degree of accuracy) all the state-feedback closed loop properties with a single observer based controller when the subsystem from the exogenous input to the measured output satisfies a minimum phase assumption.