Existence of unknown input observers and feedback passivity for linear systems

Abstract

The existence conditions of unknown input observers (UIO) for LTI systems are well known and several methods for its design have been proposed in the literature. Passivity is an important system property and has a central position in control theory. The possibility of rendering a system passive by feedback has been throughly studied and necessary and sufficient conditions for this have been obtained. In this paper it is shown that if a LTI system has an UIO, then it can be rendered strictly dissipative (or passive plus a squared down output) by either output injection or state feedback, if stabilizability is assumed in the last case. Furthermore, these properties are equivalent to a strong detectability property and to the possibility of obtaining an stable inverse of the system, by using only one derivative of the output. This allows an interesting and surprising characterization of the existence of UIO in system terms and sheds also some light into further properties of output injection or feedback passive systems. Lyapunov-like characterizations of these properties can also be given.