Simultaneous performance achievement via compensator blending

In this paper we consider the problem of designing a state-feedback controller that simultaneously achieves different optimality criteria defined on different input–output pairs. Precisely, if r “optimal” target transfer functions are given (as the result of local “optimal” controllers), it is shown that (under mild assumptions) there exists a unique controller capable of replicating these transfer functions in the closed-loop system, so simultaneously achieving the performances inherited by the chosen local transfer functions. An explicit and constructive procedure (we refer to such procedure as “compensator blending”) is provided. The possibility of designing a stable blending compensator or the generalization to dynamic local controllers or time varying systems are also discussed. We finally consider the dual version of the problem, precisely, we show how to achieve simultaneous optimality by filter blending.