This correspondence presents a relaxation of some earlier linear matrix inequality (LMI) conditions, which allow setting up less conservative stability or performance conditions for Takagi-Sugeno fuzzy models. Unlike the previous literature, this correspondence takes into account the knowledge of the membership functions' shape by considering bounds on them and their cross products (interpreted as an overlap measure), introducing auxiliary LMI variables. Numerical examples illustrate the achieved improvements.

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Current fuzzy control research tries to obtain the less conservative conditions to prove stability and performance of fuzzy control systems. In many fuzzy models, membership functions with multiple arguments are defined as the product of simpler ones, where all possible combinations of such products conform a fuzzy partition. In particular, such situation arises with widely-used fuzzy modelling techniques for non-linear systems. These type of fuzzy models will be denoted as tensor-product fuzzy systems, because its expressions can be understood as operations on multi-dimensional arrays. This paper discusses the generalisation to tensor-product fuzzy systems of the results in [5,18]. The procedures here will allow to set up LMI conditions which are less conservative than the cited ones, by exploiting the tensor-product structure of the membership functions. A numerical example illustrates the achieved improvement.

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SUMMARYRobust λ-contractive sets have been proposed in previous literature for uncertain polytopic linear systems. It is well known that, if initial state is inside such sets, it is guaranteed to converge to the origin. This work presents the generalization of such concepts to systems whose behaviour changes among different linear models with probability given by a Markov chain. We propose sequence-dependent sets and associated controllers which can ensure a reliability bound when initial conditions are outside the maximal λ-contractive set. Such reliability bound will be understood as the probability of actually reaching the origin from a given initial condition without violating constraints. As initial condition are further away from the origin, the likelihood of reaching the origin decreases.

Revista: IEEE Transactions onextend the idea to fuzzy polynomial models, by using a Taylor-series approach which expresses non-polynomial nonlinearities (or high-degree polynomial ones) as a convex interpolation between polynomials of reduced degree.Once locally exact fuzzy models are available, stability and control design for the original nonlinear system via convex optimization (particularly with Linear Matrix Inequalities (LMI)) has been deeply explored in literature. Indeed, global stability conditions for Takagi However, one of the key issues in practical usefulness of many of the above results is the fact that, given the locality

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.2013 Published by Elsevier Ltd.

Registro de acceso restringido Este recurso no está disponible en acceso abierto por política de la editorial. No obstante, se puede acceder al texto completo desde la Universitat Jaume I o si el usuario cuenta con suscripción. Registre d'accés restringit Aquest recurs no està disponible en accés obert per política de l'editorial. No obstant això, es pot accedir al text complet des de la Universitat Jaume I o si l'usuari compta amb subscripció. Restricted access item This item isn't open access because of publisher's policy. The full--text version is only available from Jaume I University or if the user has a running suscription to the publisher's contents.