This paper addresses the problem of unknown input estimation for a class of nonlinear systems with mixed nonlinear terms, namely Linear Parameter Varying (LPV) parts and purely Lipschitz nonlinearities. Three new unknown input estimation algorithms are proposed, where each algorithm depends on the distribution of the unknown inputs in the system. These algorithms provide estimation of the maximum possible unknown inputs in a system, contrarily to the methods available in the literature, which consider only particular cases. Before introducing these estimation algorithms, a general LMI-based observer design methodology is provided, as a preliminary result, for a class of nonlinear descriptor systems with nonlinear outputs. To this end, a specific Lyapunov function is exploited to avoid derivatives of the disturbances. The proposed LMI conditions are less conservative than those existing in the literature. This is due to the specific Lyapunov function, the use of Young inequality in a judicious way, and the reformulation of the Lipschitz inequality. The proposed algorithms are applied to a wastewater treatment model to show their effectiveness and performances.
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