Passivity-based robust control of non-square linear systems using a parallel feedforward compensator

We present a state-space approach to design a passivity-based dynamic output feedback control of a set of non-square linear systems. We first determine a squaring gain matrix and an additional dynamics that is connected to the systems in a feedforward way, then a static passivating control law is designed. Consequently, the actual feedback controller will be the static control law combined with the feedforward dynamics. A necessary and sufficient condition for the existence of the parallel feedforward compensator (PFC) is given by the static output feedback formulation, which enables us to utilize a linear matrix inequality (LMI). Since the proposed PFC has the same dimension with the input of the given system, our design procedure also can be viewed as a solution to the low-order dynamic output feedback control problem in literature. The effectiveness of the proposed method is illustrated by some examples.