Balanced truncation for linear interconnected systems: the state feedback case

Model order reduction is an important tool in control systems theory. In particular, it is useful for controller design since the dimension of the controller becomes very high when we use advanced control theory. Balanced truncation is one of the most useful model order reduction methods. In general, however, the stability of the feedback system is not maintained when the order of the controller is reduced by balanced truncation. This paper proposes a novel method of state feedback controller reduction by which we can preserve the stability of the resulting reduced order state feedback system. A numerical example demonstrates the effectiveness of the proposed method.