Sampled-Data Control for a Class of Singular Takagi-Sugeno Fuzzy Systems with Application in Truck-Trailer System

Abstract

In order to solve the admissibility problem for a class of nonlinear singular systems with sampling, nonlinearity, and external disturbances, a sample-data control algorithm based on input delay methodology is proposed in this paper. Firstly, the system is converted to a time-delay system based on Takagi–Sugeno fuzzy models via an input delay approach, with many novel time-delay methods being used to deal with the sampled-data control problem. Secondly, both the upper and lower bounds of the sampling period are considered, which has a wider application scope. Thirdly, to obtain less conservative results, an appropriate Lyapunov–Krasovskii function, which involves several symmetric positive definite matrices, is established, and a relaxation variable is introduced by the method of reciprocally convex inequality. Then the conditions of admissibility are given, and the design method of the sampled-data controller is introduced. Finally, a truck-trailer example and two numerical examples are given to prove that the proposed approaches are valid and applicable.