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Analysis of time-delay systems via shifted Chebyshev polynomials of the first and second kinds. (English) Zbl 0652.93029

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.

MSC:

93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
34K35 Control problems for functional-differential equations
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
44A45 Classical operational calculus
93C05 Linear systems in control theory
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References:

[1] DOI: 10.1109/TCS.1978.1084534 · Zbl 0397.93009 · doi:10.1109/TCS.1978.1084534
[2] DOI: 10.1080/00207728508926770 · Zbl 0586.93008 · doi:10.1080/00207728508926770
[3] DOI: 10.1109/TAC.1978.1101888 · Zbl 0388.93029 · doi:10.1109/TAC.1978.1101888
[4] DOI: 10.1080/0020718508961193 · Zbl 0562.93034 · doi:10.1080/0020718508961193
[5] DOI: 10.1115/1.3140675 · Zbl 0525.93036 · doi:10.1115/1.3140675
[6] DOI: 10.1007/BFb0041228 · doi:10.1007/BFb0041228
[7] DOI: 10.1115/1.3139626 · Zbl 0446.93051 · doi:10.1115/1.3139626
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