Universal Zero Dynamics: The SISO Case

Given a single-input, single-output (SISO) system with a Chen-Fliess series representation whose generating series has a well defined relative degree, it is shown that there is a notion of universal zero dynamics that describes a set of dynamics evolving on a locally convex (infinite dimensional) Lie group so as to render the system's output exactly zero. Minimum phase in this setting is defined in terms of the boundedness of the applied input which zeros the output. As an application, it is shown that one can design a zero dynamics attack on cyber-infrastructure using only an estimate of the plant's generating series. That is, detailed knowledge of the plant's internal dynamics is not needed.