Comments on "Controller Synthesis of Fuzzy-Dynamic Systems Based on Piecewise Lyapunov Functions

This comment tries to describe a theoretical mistake made in the aforementioned paper [G. Feng, IEEE Trans. Fuzzy Syst., vol. 11, no. 5, pp. 605-612, Oct. 2003] to formulate the inverse of matrices used to construct the piecewise-quadratic Lyapunov functions. Derivation of these inverse matrices is the most critical step toward transforming the design constraints into linear matrix inequalities (LMIs). Therefore, the erroneous formulation essentially affects the validity of the approach and final results. Unfortunately, it seems that there is no simple correction for this problem. However, some close alternative approaches are suggested by the same authors in their other works.