Design of unknown input observers for nonlinear systems with full and partial information

The problem of designing Unknown Input Observers (UIOs) for nonlinear systems is approached in this paper, in the cases of full and partial information. In the former, it is shown that the construction hinges upon the solution of a system of first-order Partial Differential Equations (PDEs). Such system admits a trivial solution that however renders the observer completely insensitive to disturbances as well as additional control inputs, which is a rather undesirable property in the application of UIOs to the context of Fault Detection. Therefore, we propose an alternative design methodology that allows to extend the set of solutions to the above PDEs by relying merely on the solution of ordinary differential equations, namely by exploiting the Theory of Characteristics. Then, in the partial information scenario, it is shown that introducing a suitable change of coordinates and considering reduced-order observers permit the decomposition of the primary task of disturbance decoupling with that of asymptotic stability, hence providing more intuitive conditions for the observer design.