Suboptimal control of linear delay systems via Legendre series

Mohsen Razzaghi; M. F. Habibi; R. Fayzebakhsh

Kybernetika (1995)

  • Volume: 31, Issue: 5, page 509-518
  • ISSN: 0023-5954

How to cite


Razzaghi, Mohsen, Habibi, M. F., and Fayzebakhsh, R.. "Suboptimal control of linear delay systems via Legendre series." Kybernetika 31.5 (1995): 509-518. <>.

author = {Razzaghi, Mohsen, Habibi, M. F., Fayzebakhsh, R.},
journal = {Kybernetika},
keywords = {suboptimal control; linear delay systems; quadratic cost; Legendre series; necessary condition of optimality},
language = {eng},
number = {5},
pages = {509-518},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Suboptimal control of linear delay systems via Legendre series},
url = {},
volume = {31},
year = {1995},

AU - Razzaghi, Mohsen
AU - Habibi, M. F.
AU - Fayzebakhsh, R.
TI - Suboptimal control of linear delay systems via Legendre series
JO - Kybernetika
PY - 1995
PB - Institute of Information Theory and Automation AS CR
VL - 31
IS - 5
SP - 509
EP - 518
LA - eng
KW - suboptimal control; linear delay systems; quadratic cost; Legendre series; necessary condition of optimality
UR -
ER -


  1. M. Jamshidi, C. M. Wang, A computational algorithm for large-scale nonlinear time-delays systems, IEEE Trans. Systems Man Cybernet. SMC-14 (1984), 2-9. (1984) MR0740948
  2. G. L. Kharatishvili, The maximum principle in the theory of optimal process with time-lags, Dokl. Akad. Nauk SSSR 136 (1961), 39-42. (1961) MR0123073
  3. K. Inoue H. Akaski K. Ogino, Y. Sawaragi, Sensitivity approaches to optimization of linear system with time delay, Automatica 7 (1971), 671-679. (1971) MR0320869
  4. M. Jamshidi, M. Razzaghi, Optimization of linear systems with input time-delay, Kybernetika 11 (1975), 375-384. (1975) Zbl0333.49036MR0446641
  5. M. MaleK-Zavarei, Near-optimum design of nonstationary linear systems with state and control delays, J. Optim. Theory Appl. 50 (1980), 73-88. (1980) Zbl0394.49017MR0562197
  6. M. S. Corrington, Solutions of differential and integral equations with Walsh functions, IEEE Trans. Circuit Theory 20 (1973), 470-476. (1973) 
  7. C. Hwang, Y. P. Shih, Optimal control of delay systems via block pulse functions, J. Optim. Theory Appl. 45 (1985), 101-112. (1985) Zbl0541.93031MR0778160
  8. P. N. Paraskevopoulo P. G. Sklavounos, G. Ch. Georgiou, The operation matrix of integration for Bessel functions, J. Franklin Inst. 557 (1990), 329-341. (1990) MR1042680
  9. C. Hwang, Y. P. Shih, Solution of integral equations via Laguerre polynomias, Comput. Electr. Engrg. 9 (1982), 123-129. (1982) 
  10. M. Razzaghi, M. Razzaghi, Solution of linear two-point boundary value problems and optimal control of time-varying systems by shifted Chebyshev approximations, J. Franklin Inst. 557 (1990), 321-328. (1990) Zbl0714.49032MR1042679
  11. I. R. Horng, J. H. Chou, Analysis, parameter estimation and optimal control of time-delay systems via Chebyshev series, Internat. J. Control 41 (1985), 1221-1234. (1985) Zbl0562.93034MR0792938
  12. M. H. Perng, Direct approach for the optimal control of linear time-delay systems via shifted Legendre polynomials, Internat. J. Control 43 (1986), 1897-1904. (1986) Zbl0586.93026
  13. M. Razzaghi M. Razzaghi, and A. Arabshahi, Solutions of convolution integral and Fredholm integral equation via double Fourier series, Appl. Math. Comput. 40 (1990), 215-224. (1990) MR1082397
  14. C. Hwang, M. Y. Chen, A direct approach using the shifted Legendre series expansion for near optimum control of linear time-varying systems with multiple state and control delays, Internat. J. Control 43 (1986), 1673-1692. (1986) Zbl0586.93048
  15. I. S. Gradshteyn, I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York 1979. (1979) 
  16. C. Canuto M. Y. Hussaini, and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, New York 1988. (1988) MR0917480
  17. P. Lancaster, Theory of Matrices, Academic Press, New York 1969. (1969) Zbl0186.05301MR0245579

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