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 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.