Analysis of time-delay systems via shifted Chebyshev polynomials of the first and second kinds

A novel and general approach for obtaining the delay operational matrix of shifted Chebyshev polynomials of first or second kind is presented. This operational matrix is exact in the sense that it does not involve any approximation. Next, this paper shows the application of the delay operational matrix in the analysis of time-delay systems. Two illustrative examples are included and the results are compared with those obtained by the exact method.