SOS-based stability analysis of takagi-sugeno fuzzy control systems via polynomial membership functions

This paper presents stability analysis of fuzzy-model-based control systems using sum-of-squares (SOS) approach. Based on the T-S fuzzy model, a fuzzy controller is employed to close the feedback loop to form a FMB control system. It is assumed that the membership functions of T-S fuzzy model and fuzzy controller are not necessarily the same. One of the drawbacks in the existing approaches is that the information of membership functions are not brought into stability analysis. Then the stability conditions are valid for any shape of membership functions. As a result it may lead to conservative stability conditions. To take the membership functions´ information into stability analysis, SOS approach is employed. The operating domain of membership functions is partitioned to sub-regions. Then corresponding to each product term of membership functions in each sub-region an approximated polynomial is derived to facilitate the stability analysis. Based on the derived conditions in all of the sub-regions applying the Lyapunov stability, SOS-based conditions are derived. The solution of the SOS-based stability conditions can be found effectively using the SOSTOOLS which is a free third-party MATLAB Toolbox. Numerical example is given to illustrate the effectiveness of the proposed stability conditions.