On the Zero Dynamics of Linear Input-Output Models.

Zeros are of extreme importance in linear systems theory, especially unstable zeros, which degrade achievable performance. Furthermore, the presence of a zero in a state-space model implies the existence of an initial condition and a nonzero input signal such that the output is identically zero; this property is calledoutput zeroing. The purpose of this paper is to elucidate the properties of the zero dynamics within the context of input-output models, which, like state-space models, are time-domain models, but, unlike state-space models, have no internal state. In particular, the focus is on the zero dynamics of left polynomial fraction description (LPFD) input-output models whose denominator polynomial is not necessarily monic.