Stability and stabilization conditions for Takagi-Sugeno fuzzy model via polyhedral Lyapunov functions

Polyhedral Lyapunov functions (PLFs) are universal for establishing stability of Takagi-Sugeno (T-S) fuzzy models. In this paper, a stability theorem via PLFs is presented for T-S models, and it is shown that stability can be established via linear programming. Furthermore, nonconvex stabilization conditions are stated that, if satisfied, specify a parallel distributed compensation (PDC) controller as well as a PLF which proves stability of the closed loop system. An algorithm is presented as an initial step in working around the nonconvex stabilization conditions, and has shown to be useful in the computation of PDC controllers.