Paraskevopoulos, P. N.; Sparis, P. D.; Mouroutsos, S. G. The Fourier series operational matrix of integration. (English) Zbl 0558.44004 Int. J. Syst. Sci. 16, 171-176 (1985). A general expression of the Fourier series operational matrix of integration P is derived. This matrix has most of its elements zero, a fact which makes this matrix computationally appealing. Furthermore, due to the integral properties of the sine and cosine functions, the approximation involved in \(\int^{t}_{a}...\int^{t}_{a}\phi (\sigma)(d\sigma)^ k\approx P^ k\phi (t)\) could be better as compared to other orthogonal functions for example the Walsh functions. This matrix P may be used to solve problems like identification, analysis and optimal control. Reviewer: S.P.Goyal Cited in 60 Documents MSC: 44A45 Classical operational calculus 93E12 Identification in stochastic control theory 93C15 Control/observation systems governed by ordinary differential equations 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. Keywords:matrix of integration; Fourier operational matrix; orthogonal functions; Walsh; block-pulse; Laguerre; Legendre; Chebyshev; identification; optimal control; system analysis PDFBibTeX XMLCite \textit{P. N. Paraskevopoulos} et al., Int. J. Syst. Sci. 16, 171--176 (1985; Zbl 0558.44004) Full Text: DOI References: [1] CHEN C. F., I.E.E.E. Trans. autom. Control 20 pp 596– (1975) · Zbl 0317.49042 · doi:10.1109/TAC.1975.1101057 [2] CHURCHILL R. V., Fourier Series and Boundary Value Problems (1941) · Zbl 0025.05403 [3] HWANG C., Int. J. Systems Sci. 13 pp 209– (1982) · Zbl 0475.93033 · doi:10.1080/00207728208926341 [4] KING R. E., Int. J. Control 30 pp 1023– (1979) · doi:10.1080/00207177908922832 [5] PARASKEVOPOULOS P. N., J. Franklin Inst. 316 pp 135– (1983) · Zbl 0538.93013 · doi:10.1016/0016-0032(83)90082-0 [6] PARASKEVOPOULOS P. N., Proc. 1983 AMSE Conf. Conf. on Modelling and Simulation (1983) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.