Polytopic invariant and contractive sets for closed-loop discrete fuzzy systems |
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| Authors: | Carlos Ariño Emilio Pérez Antonio Sala Fernando Bedate |
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| Institution: | 1. Departamento de Ingeniería de Sistemas Industriales y Diseño, Universitat Jaume I, Avenida Vicent Sos Baynat, s/n. 12071 Castelló de la Plana, Spain;2. Instituto Universitario de Automática e Informática Industrial, Universidad Politécnica de Valencia, Camino de Vera, S/N 46022 Valencia, Spain |
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| Abstract: | In this work a procedure for obtaining polytopic λ-contractive sets for Takagi–Sugeno fuzzy systems is presented, adapting well-known algorithms from literature on discrete-time linear difference inclusions (LDI) to multi-dimensional summations. As a complexity parameter increases, these sets tend to the maximal invariant set of the system when no information on the shape of the membership functions is available. λ-contractive sets are naturally associated to level sets of polyhedral Lyapunov functions proving a decay-rate of λ. The paper proves that the proposed algorithm obtains better results than a class of Lyapunov methods for the same complexity degree: if such a Lyapunov function exists, the proposed algorithm converges in a finite number of steps and proves a larger λ-contractive set. |
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