Observers for a class of Lipschitz systems with extension to performance analysis |
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Authors: | Ali Zemouche Mohamed Boutayeb G Iulia Bara |
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Affiliation: | aLSIIT-UMR CNRS-ULP 7005, ENSPS, Bd. Sébastien Brant, BP 10413, 67412 Illkirch Cedex, France |
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Abstract: | In this paper, 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 of introducing a general Lipschitz-like condition on the Jacobian matrix for differentiable systems. To ensure asymptotic convergence, in both continuous and discrete time systems, such sufficient conditions expressed in terms of linear matrix inequalities (LMIs) are established. An extension to H∞ filtering design is obtained also for systems with nonlinear outputs. A comparison with respect to the observer method of Gauthier et al. A simple observer for nonlinear systems. Applications to bioreactors, IEEE Trans. Automat. Control 37(6) (1992) 875–880] is 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 with the goal to illustrate good performances on robustness to measurement errors by avoiding high gain. |
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Keywords: | Nonlinear systems Observer design Linear parameter varying (LPV) systems LMI solution Differential mean value theorem (DMVT) color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V4X-4PDK461-1&_mathId=mml49&_user=10&_cdi=5770&_rdoc=4&_acct=C000053510&_version=1&_userid=1524097&md5=1222a73600b3e60569273e5e38599254" title="Click to view the MathML source" H∞" target="_blank">alt="Click to view the MathML source">H∞ performance analysis |
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