Membership-function-dependent stability analysis and local controller design for T–S fuzzy systems: A space-enveloping approach

For Takagi–Sugeno (T–S) fuzzy systems, relaxed stability conditions are obtained by more effectively enveloping the trajectory of membership functions (MFs) in a unified space MF. Considering an open-loop T–S system, system premise variables operation domain can be divided into series subdomains. Based on MF extremum calculation technique, MFs values each variable corresponding to subdomain calculated. With these extremes, tight local convex polyhedron is constructed subdomain. Thus, linear matrix inequality (LMI) derived via piecewise Lyapunov function. Then, state-feedback controller designed close loop. From geometric viewpoint, and linear-approximation methods both utilized achieve robustness conditions. Finally, several examples adopted illustrate metrics proposed approaches.