Control Design for Interval Type-2 Takagi-Sugeno Singular Systems with Time Delay

Abstract In this work, the admissibility analysis and the control problem are investigated for nonlinear singular systems represented by interval type-2 Takagi-Sugeno (T-S) fuzzy models with time delay. First, the interval type-2 fuzzy singular systems with time delay have been described. Second, the admissibility analysis of the autonomous singular systems is studied. Third, the control problem has been investigated. For this, an interval type-2 fuzzy control law is designed to guarantee the admissibility of the closed-loop system despite the presence of uncertainties and time delay. To demonstrate the existence of the proposed controller, by using generalised integral inequalities, sufficient delay-dependent conditions are given in terms of Linear Matrix Inequalities (LMIs). Finally, an application to inverted pendulum system presented by interval type-2 fuzzy models is afforded to show the effectiveness of the suggested method.