A Characterization of All Passivizing Input-Output Transformations of a Passive-Short System

Passivity theory is one of the cornerstones of control theory, as it allows one to prove stability of a large-scale system while treating each component separately. In practice, many systems are not passive, and must be passivized in order to be included in the framework of passivity theory. Input-output transformations are the most general tool for passivizing systems, generalizing output-feedback and input-feedthrough. In this paper, we classify all possible input-output transformations that map a system with given shortage of passivity to a system with prescribed excess of passivity. We do so by using the connection between passivity theory and cones for SISO systems, and using the S-lemma for MIMO systems. We also present several possible applications of our results.

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