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Observers for a class of Lipschitz systems with extension to H-infinity performance analysis

Abstract : In this note, observer design for a class of Lipschitz nonlinear dynamical systems is investigated. One of the main contributions lies in the use of the Differential Mean Value Theorem (DMVT) which allows transforming the nonlinear error dynamics into a Linear Parameter Varying (LPV) system. This has the advantage to introduce a general Lipschitz-Like condition on the Jacobian matrix for differentiable systems. To ensure asymptotic convergence, in both continuous and discrete time systems, suit sufficient conditions expressed in terms of Linear Matrix Inequalities (LMIs) are established. An extension to H-infinity filtering design is obtained also for systems with nonlinear outputs. A comparison with respect to the observer method of Gauthier et al (1992) presented to show that the proposed approach avoids high gain for a class of triangular globally Lipschitz systems. In the last section, academic examples are given to show the performances and some limits of the proposed approach. The last example is introduced in the goal to illustrate good performances on robustness to measurement errors by avoiding high gain.
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Contributor : Michel Zasadzinski Connect in order to contact the contributor
Submitted on : Thursday, December 4, 2008 - 7:31:53 PM
Last modification on : Thursday, April 23, 2020 - 2:26:30 PM

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Ali Zemouche, Mohamed Boutayeb, Iula Bara. Observers for a class of Lipschitz systems with extension to H-infinity performance analysis. Systems and Control Letters, 2008, 57 (1), pp.18-27. ⟨10.1016/j.sysconle.2007.06.012⟩. ⟨hal-00344476⟩



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