In this paper the H∞ observers design problem for a class of discrete time Lipschitz nonlinear singular systems is considered. The approach is based on the parameterization of the obtained algebraic constraints from the estimation errors. Sufficient conditions for the existence of the observers which guarantee stability and the worst case observers error energy over all bounded energy disturbances is minimized are given. The method also unifies the design for the fullorder, reduced-order, minimal-order observers for discrete time systems. Application to standard systems with unknown input is presented via a numerical example.

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An accurate battery management strategy is a crucial need in the developing of reliable and viable plug in and hybrid electric vehicles. This on-board algorithm has the advantages to protect the battery from critical operating conditions and improve its lifetime. However, the effectiveness of the battery management strategy mainly depends on the accuracy of its state of charge (SOC). In this context, this paper proposes a novel technique for the SOC estimation based on the unknown input observer and a new differential-algebraic model of a lithium iron phosphate battery. The proposed observer aims to overcome the unknown value of the initial SOC for on-board batteries using only current and terminal voltage measurements. A reduced-order based unknown input observer is developed to estimate the open circuit voltage and the SOC using the OCV-SOC characteristic offline-determined. The unbiasedness of the estimation error is guaranteed by the parameterization of a set of Sylvester constraints. The performance of the proposed observer is verified by simulations and experiments and the accuracy of the obtained results is analyzed and assessed.