Existence of unknown input observers and feedback passivity for linear systems

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. These systems are able to estimate perfectly the state of the system despite of completely unknown input perturbations, i.e. they are robust to arbitrary disturbances, and play a key role in areas such as fault detection and isolation, descentralized control, and robust observers. Passivity is an important system property and has a central position in control theory. Recently the possibility of rendering a system passive. by feedback (Feedback Passivity) 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 sheeds also some light into further properties of output injection or feedback passivizable systems. Lyapunov-like characterizations of these properties can also be given.