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Solutions of TS Fuzzy Model Based Time-Delay Dynamic Systems via Chebyshev Series Approach

A shifted Chebyshev series approach for solve the Takagi-Sugeno (TS) fuzzy model based time-delay dynamic equations (TSFMTDE) is developed in this article. The new method simplifies the procedure of solving the TSFMTDE into the solution of a system of recursive formulae involving only matrix algebra. An algorithm based on these recursive formulae, and including only straightforward algebraic computation is also proposed in this article. The new approach proposed is non-iterative, non-differential, non-integral, straightforward, and well-adapted to computer implementation. Two numerical examples are provided. The first shows that the proposed method based on the shifted Chebyshev series may yield close-to-exact solutions. The second (a nonlinear mass-spring-damper mechanical time-delay system with a fuzzy parallel-distributed-compensation controller) demonstrates the application of the proposed approach.