Design of general structured observers for linear systems with unknown inputs

Using the framework of the general structured (GS) observer, we present a straightforward procedure for designing an unknown input observer (UIO) for a linear system subject to unknown inputs or uncertain disturbances. The set of all GS observers insensitive to unknown inputs is derived in this paper. Moreover, an extension of the UIO, called the extended UIO, is developed to estimate both the system state and the unknown input simultaneously. We show the existence conditions of a stable UIO are the same as those of a stable left inverse system. In addition, well-conditioned designs for both the state and unknown input estimations are also explored. Conditions of transmission zeros reveal that to achieve a stable UIO, the uncertain system should be minimum-phase. To overcome this restriction, we adopt a two-delay output stabilized method to design the stabilized UIO without implementing extra sensors. Experimental results for a DC servo motor system demonstrate the applicability of the proposed methodologies.