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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 [Formula: see text] 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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In this paper we investigate the problem of the design of a controller based on H∞ functional filter, in a finite time stability context for linear continuous time-invariant systems affected by norm bounded disturbances. The finitetime H∞ boundedness criterion of the closed-loop system is investigated. The order of the controller is reduced since the designed functional filter has the same order than the dimension of the control input of the system. The design conditions are expressed as linear matrix inequalities. A numerical example is provided to show the validity of the proposed approach.978-1-4799-8318-6/15/$31.00 ©2015 IEEE