Abstract
This chapter investigates the stabilization of two-dimensional (2-D) Takagi–Sugeno (T–S) systems with stochastic perturbations. Our aim is to develop state feedback controllers that ensure mean-square stabilization and a guaranteed level of attenuation for the perturbations expressed as an \(H_{\infty }\) norm. Sufficient conditions are derived for the existence of such controls in terms of linear matrix inequalities (LMIs) that make it possible to solve the corresponding control synthesis problem. Numerical examples are given to demonstrate the effectiveness of the proposed method.
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Benzaouia, A., Hmamed, A., Tadeo, F. (2016). Stabilization of Two-Dimensional Takagi–Sugeno Systems with Attenuation of Stochastic Perturbations. In: Two-Dimensional Systems. Studies in Systems, Decision and Control, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-20116-0_7
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DOI: https://doi.org/10.1007/978-3-319-20116-0_7
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