LMI-based stability analysis of fuzzy model-based control systems using approximated polynomial membership functions

Relaxed LMI-based stability conditions for fuzzy model-based (FMB) control systems with imperfect premise matching are proposed. Information of membership functions containing relations between state variables and membership functions are taken into stability analysis. Firstly, based on the Lyapunov stability theorem, derivative of quadratic Lyapunov function containing product terms of fuzzy model and fuzzy controller's membership functions are derived. Then, the operating domain of membership functions is partitioned to sub-regions, such that each product term of fuzzy model and fuzzy controller membership functions is approximated properly with a polynomial of state variables. Next, in each sub-region LMI-based stability conditions containing the information of subsystems and approximated polynomials are derived. It is shown that the previous stability conditions can be as special cases of the proposed stability conditions. Finally, simulation example is given to illustrate the validity and effectiveness of the proposed approach.