Relaxed LMI conditions for closed-loop fuzzy systems with tensor-product structure

Current fuzzy control research tries to obtain the less conservative conditions to prove sta-bility and performance of fuzzy control systems. In many fuzzy models, membership func-tions 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 un-derstood 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. Key words: fuzzy control, linear matrix inequalities, fuzzy modelling