Geodesic
An adaptive observer design approach for a class of discrete-time nonlinear systems
International Journal of Applied Mathematics and Computer Science, Tome 28 (2018) no. 1, pp. 55-67.

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We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems that could be transformed into a quasi-LPV (linear parameter varying) polytopic model in the Takagi–Sugeno (T–S) form. Such systems could have unmeasured premise variables, a case usually overlooked in the observer design literature. We assert that, for such systems in discrete-time, the current literature lacks design strategies for joint state and parameter estimation. To this end, we adapt the existing literature on continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear systems. A Lyapunov approach is used to illustrate stability, and bounds for the estimation error are obtained via the bounded real lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear systems with constant parameters. This results in less conservative conditions and a simplified design procedure. A basic waste water treatment plant simulation example is discussed to illustrate the design procedure.
Keywords: adaptive observer, joint state estimation, parameter estimation, Takagi-Sugeno model, time-varying parameter estimation, sector nonlinearity transformation, discrete-time nonlinear systems
Mots-clés : obserwator adaptacyjny, identyfikacja parametrów, model Takagi-Sugeno, transformacja nieliniowa, dyskretny układ nieliniowy 
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Srinivasarengan, K.; Ragot, J.; Aubrun, C.; Maquin, D. An adaptive observer design approach for a class of discrete-time nonlinear systems. International Journal of Applied Mathematics and Computer Science, Tome 28 (2018) no. 1, pp. 55-67. http://geodesic.mathdoc.fr/item/IJAMCS_2018_28_1_a3/

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