Model Matching and Passivation of MIMO Linear Systems via Dynamic Output Feedback and Feedforward

A model matching and passivating control architecture for multi-input/multi-output linear systems, comprising dynamic feedback and feedforward, is proposed. The approach—essentially without any restriction on the relative degree and the zeros of the underlying system and by relying only on input/output measurements—provides a closed-loop system, the transfer matrix of which matches any desired matrix of rational functions. An alternative implementation of the above design allows to achieve an arbitrary approximation accuracy of a desired transfer matrix while also preserving structural properties—in particular observability—of the overall interconnected system. Such a construction can be then specialized to provide input/output decoupling or a system that is passive from a novel control input to a modified output. The result is achieved by arbitrarily assigning the relative degree and location of the poles and zeros on the complex plane of the interconnected system in a systematic way. It is also shown that similar ideas can be employed to enforce a desired, arbitrarily small, $\mathcal {L}_2$-gain from an unknown disturbance input to a modified output, while preserving the corresponding gain from the control input to the same output. The article is concluded with applications and further discussions on the results.