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LMI-based adaptive control for uncertain polytopic systems

Abstract : Despite the similarities between polytopic uncertain systems and Takagi-Sugeno fuzzy models, there is a fundamental difference: the exact knowledge of the linear systems weighting functions (also known as membership functions in the fuzzy systems literature). This knowledge is usually incorporated into fuzzy control laws, which allows for less conservative controllers. This work proposes a novel set of LMI synthesis conditions which when feasible guarantees that an adaptive control law, mimicking a fuzzy control law, asymptotically stabilizes the uncertain polytopic system. A numerical example is presented to demonstrate the effectiveness of the proposed control law.
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Victor Campos, Tran Anh-Tu Nguyen, Reinaldo Martinez Palhares. LMI-based adaptive control for uncertain polytopic systems. 2016 IEEE 55th Conference on Decision and Control (CDC), Dec 2016, Las Vegas, United States. pp.3222-3227, ⟨10.1109/CDC.2016.7798753⟩. ⟨hal-03415303⟩



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