This paper uses Linear Matrix Inequality (LMI) techniques to apply regional eigenvalue assignment constraints to a dynamic state-feedback controller design for discrete-time systems with vanishing nonlinear perturbations. The controller design also incorporates the H∞ performance criterion. The regional eigenvalue assignment place the eigenvalues of the linear part of the system in two distinct regions, one region for the controller eigenvalues and one region for the observer eigenvalues, in such a way that the state estimation error goes to zero significantly faster than the state reaches steady state.

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