In this note, we investigate the problem of state observation and input recovery of a particular class of nonlinear systems based on multi-models with unknown input. For this particular system and a corresponding observer structure, an original set of sufficient LMI conditions are derived from the Lyapunov theory, allowing to compute the gains of the observers and assuring asymptotic convergence. A numerical example is given in the context of secure communication, showing the practical interest of the method.Index Terms-Unknown input observer, Discrete-time multimodel system, Lipschitz nonlinear system, linear matrix inequalities.

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