Robust stability and stabilisation for nonlinear uncertain time-delay systems via fuzzy control approach

The problems of robust stability analysis and synthesis of uncertain nonlinear systems with time-varying delays and norm-bounded uncertainties via linear Takagi–Sugeno fuzzy model approach are discussed. First, a delay-dependent robust stability criterion is derived within the framework of linear matrix inequalities. The relationships between the terms in the Leibniz–Newton formula and the system matrices are taken into account. Then the stabilisation approach for nonlinear delayed systems through fuzzy state feedback is presented. Several examples show the proposed method to be a significant improvement over the existing ones.