Improved LMI-based conditions for quadratic stabilization of Takagi-Sugeno fuzzy systems

This note is concerned with quadratic stabilization problem of continuous nonlinear control system given by Takagi-Sugeno(T-S) fuzzy models. It provides improved linear matrix inequality (LMI)-based conditions to compute a T-S state-feedback gain that makes closed-loop system quadratically stable. The proposed conditions are based on the philosophy of Polyapsilas theorem and on the systematic construction of homogeneous polynomial solution for parameter-dependent LMI. Compared with the existing methods in the literature, these new conditions can provide less conservative or at least the same results. Finally, a simple numerical example is given to illustrate the effectiveness of the proposals.