A Characterization of All Linear Passivizing Input-Output Transformations of a Passive-Short System: The SISO Case

Passivity theory is one of the cornerstones of control theory providing a systematic way to study the stability of interconnected systems. It is well known that many systems are not passive, and must be passivized in order to be included in the framework of passivity theory. Input-output (loop) transformations are the most general tool for passivizing systems. In this letter, we propose a characterization of 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.