Stabilization of Takagi-Sugeno model via non-parallel distributed compensation law

This paper addresses the stabilization of nonlinear systems represented by a discrete-time Takagi-Sugeno (T-S) model. Based on the extended nonquadratic Lyapunov function and the non-parallel distributed compensation law, the improvement over the existing results is achieved via introducing new slack matrices, new collection matrices and the higher dimensional collection matrix. We note that T-S model is a nice platform to test various stabilization conditions solvable via linear matrix inequality techniques, and suggest future directions on this research area. The effectiveness of the new results is validated by a numerical example.