LMI-based quadratic stability analysis for hierarchical fuzzy systems

The quadratic stability issue in a hierarchical fuzzy system is investigated and a Takagi-Sugeno (T-S) type hierarchical fuzzy controller is proposed to regulate the nth order linear SISO plant with the bounded time-varying uncertainties or nonlinearities. The proposed T-S type hierarchical fuzzy controller is made up of n-1 2D T-S type fuzzy controllers and allows for the simple closed dynamics in the diagonal norm-bound linear differential inclusions (DNLDI) formulation. For this closed dynamics, the stability condition in linear matrix inequalities (LMI) form is presented. Then, based on the stability condition, a method for finding the maximum stable ranges of the T-S type hierarchical fuzzy controller gains is proposed. To illustrate the performance of the proposed method, a third order simple example is given.