Decoupling of systems with feedforward matrix with application to automobile vibration system

The contribution of the paper is two fold: first the theoretical results concerning the decoupling problem of systems described by x˙=Ax+Bu, y=Cx+Du are derived (necessary and sufficient conditions, general form of controller matrices, general form and stability properties of closed-loop system). These results complement well known results in the decoupling theory which are established for the case where the feedforward matrix D=0. The authors´ results are therefore more general and cover many practical systems where D≠0. Such a practical system is an automobile vibration system. The second contribution of the paper is the application of the theoretical decoupling results to this vibration system. This case study appears to be first in the field. The decoupling controller design is simple to implement, while it yields a significant improvement in the system performance (ride comfort, road holding, riding safety, etc.)