Nonquadratic Stabilization Conditions for a Class of Uncertain Nonlinear Discrete Time TS Fuzzy Models: A New Approach

The discrete-time uncertain nonlinear models are considered in a Takagi-Sugeno form and their stabilization is studied through a non- quadratic Lyapunov function. The classical conditions consider a one- sample variation, here, the main results are obtained considering k samples variation, i.e., Delta_k V(x(t)) = V(x(t + k)) - V(x(t)). The results are shown to always include the classical cases, and several examples illustrate the effectiveness of the approach.