Stabilization of Takagi–Sugeno Model via Nonparallel Distributed Compensation Law

This paper addresses the stabilization of nonlinear systems, which is represented by a Takagi-Sugeno (T-S) model. Based on the extended nonquadratic Lyapunov function and the nonparallel distributed compensation law, three new results are obtained by using appropriate slack matrices, collection matrices, and the higher dimensional collection matrix. The first two results are less conservative, and computationally less expensive, than some of the existing results. The third result combines the procedures of the first two results, and is less conservative, but is computationally more expensive than the first two results. The effectiveness of the new results is validated by two numerical examples.