Passification of a non-square linear system is considered by using a parallel feedforward compensator (PFC) and a squaring gain matrix. In contrast to the previous result, a technical assumption is removed by modifying the structure of the PFC. As a result, the broader class of non-square systems can be made passive by the proposed design method. Using the static output feedback (SOF) algorithms, the input-dimensional PFC and the squaring matrix can be designed systematically. The effectiveness of the proposed method is illustrated by practical system examples in the control literature.

We present a state-space approach to the problem of designing a parallel feedforward compensator (PFC), which has the same dimension of the input i.e. input-dimensional, for a class of non-square linear systems such that the closed-loop system is strictly passive. For a non-minimum phase system or a system with high relative degree, passification of the system cannot be achieved by any other methodologies except by using a PFC. In our scheme, we first determine a squaring gain matrix and an additional dynamics that is connected to the system in a feedforward way, then a static passifying control law is designed. Consequently, the actual feedback controller will be the static control law combined with the feedforward dynamics. Necessary and sufficient conditions for the existence of the PFC are given by the static output feedback formulation, which enables to utilize linear matrix inequality (LMI). Since the proposed PFC is input-dimensional, our design procedure can be viewed as a solution to the low-order dynamic output feedback control problem in the literature. The effectiveness of the proposed method is illustrated by some numerical examples.