New delay-dependent finite-time stabilization of Takagi-Sugeno fuzzy approaches for delayed nonlinear systems

In this paper, the finite-time stability and stabilization of nonlinear systems with delays is studied, via a Takagi-Sugeno approach. By using a novel Lyapunov-Krasovskii functional and introducing some fuzzy free-weighting matrices, sufficient conditions are derived, for bounded and differentiable time-varying delays in terms of an upper bound of the delay derivatives. Then, we achieve closed-loop stabilization in finite time through an efficient parallel distributed compensation design. The sufficient conditions are formulated as linear matrix inequalities to achieve the desired performance. Finally, the proposed methodology is applied to various case studies, highlighting its significance.