Abstract
This chapter provides the technical and mathematical background for the fuzzy model-based control which offers the equations of the fuzzy model and closed-loop systems, definition of variables, published stability conditions in terms of linear matrix inequalities (LMIs) and sum of squares (SOS). Numerical examples are given to demonstrate the motivation using polynomial fuzzy model over T-S fuzzy model. State-feedback fuzzy controller and polynomial fuzzy controller are introduced to close the feedback loop. Three main types of control design including perfectly, partially and imperfectly matched premises are discussed and compared. LMI/SOS-based stability conditions in the literature are reviewed, which will be used in other chapters for comparison purposes.
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Lam, HK. (2016). Preliminaries. In: Polynomial Fuzzy Model-Based Control Systems. Studies in Systems, Decision and Control, vol 64. Springer, Cham. https://doi.org/10.1007/978-3-319-34094-4_2
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DOI: https://doi.org/10.1007/978-3-319-34094-4_2
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