Unknown input observers for SISO nonlinear systems

The existence conditions for unknown input observers for LTI systems are well known and several methods for its design have been proposed in the literature. However, for nonlinear systems only sufficient conditions are known for certain classes of systems. In the paper sufficient conditions under which the construction of an state unknown input observer for nonlinear systems are derived. Furthermore, this conditions are also shown to be necessary, under some additional conditions. A method to design full order and reduced order unknown input observers is proposed, and its convergence is analyzed. Although in the paper the study is restricted to SISO systems, most of the results can be carried on to MIMO systems. These results are important in the design of fault detection and isolation filters, robust nonlinear observers, and decentralized control