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.