Computation of quadratic cost functionals for linear systems with multiple time delays

IEEE Transactions on Automatic Control

Volumn 45, Issue 4, 2000, Pages 800-805

  Hwang, Jyh Haur ^a   Tsay, Sun Yuan ^a   Hwang, Chyi ^b  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; INTEGRAL EQUATIONS; INVARIANCE; NUMERICAL METHODS; POLYNOMIALS; TRANSFER FUNCTIONS;

DIOPHANTINE EQUATION; EUCLID ALGORITHM; FINITE DEGREE POLYNOMIAL FACTORIZATION; LINEAR TIME INVARIANT SYSTEMS; MULTIPLE TIME DELAYS; PARTIAL FRACTION EXPANSION; QUADRATIC COST FUNCTIONALS;

LINEAR CONTROL SYSTEMS;

EID: 0034171548     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.847126     Document Type: Article

References (19)

1. D. Graham and R. C. Lathrop, "The synthesis of "optimum" transient response: Criteria and standard forms," AIEE Trans. Part II: Applicat. Ind., vol.72, pp. 273-288, 1953.
2. G. J. Murphy and N. T. Bold, " Optimization based on a square-error criterion with an arbitrary weighting function," IRE Trans. Automat. Contr., vol. 5, pp. 24-30, Jan. 1960.
3. M. Zhuang and D. P. Atherton, "Automatic tuning of optimum PID controllers," Proc. Inst. Elect. Eng. D, vol. 140, no. 3, pp. 216-224, 1993.
4. J. B. Conway, Functions of One Complex Variable, 2nd ed. New York: Springer-Verlag, 1978.
5. K. J. Astrom, Introduction to Stochastic Control Theory. New York: Academic, 1970.
6. A. W. Babister, "Determination of the optimum response of linear systems (zero displacement error systems)," Quart. J. Mech. Appl. Math., pt. 4, vol. X, pp. 504-512, 1957.
7. _, " Determination of the optimum response of linear systems (zero-velocity-error and zero-acceleration-error systems)," Quart. J. Mech. Appl. Math., pt. 1, vol. XI, pp. 119-128, 1958.
8. H. Gorecki, "The theorem concerning performance index for dynamic control systems," Bull. Polish Acad. Sci., vol. 36, no. 3/4, pp. 255-270, 1988.
9. P. Grabowski, "Evaluation of quadratic cost functionals for neutral systems: The frequency-domain approach," Int. J. Contr., vol. 49, no. 3, pp. 1033-1053, 1989.
10. K. Walton and H. Gorecki, "On the evaluation of cost functionalis with particular emphasis on time delay systems," IMA J. Math. Contr. Inform., vol. 1, no. 3, pp. 283-306, 1984.
11. K. Walton and J. E. Marshall, "Closed form solutions for time delay systems' cost functionals," Int. J. Contr., vol. 39, no. 5, pp. 1063-1071, 1984.
12. _, "Evaluation of cost functionals for systems with commensurate delays by a finite polynomial method," Proc. Inst. Elect. Eng. D, vol. 134, no. 2, pp. 108-114, 1987.
13. K. Walton, B. Ireland, and J. E. Marshall, "Evaluation of weighted functionals for time-delay systems," Int. J. Contr., vol. 44, no. 6, pp. 1491-1498, 1986.
14. C. Hwang, Y. H. Chuang, and Y. P. Shih, "Numerical computation of quadratic cost functional for linear systems with multiple delays," Contr. Comput., vol. 22, no. 3, pp. 90-95, 1995.
15. H. Gorecki and L. Popek, "Calculation of the integral squared error for large dynamic systems with many commensurate delays," Contr. Cybern., vol. 20, no. 2, pp. 33-67, 1991.
16. H. Gorecki and A. Korytowski, Advances in Optimization and Stability Analysis of Dynamical Systems. Krakow: AGH, 1993.
17. G. X. Gui, Z. Hashemi and E. B. Lee, "On calculation of the integral-squared-error for linear time-delay systems," in Proc. 24th IEEE Conf. Decision Contr., 1985, pp. 868-871.
18. J. H. Hwang, S. Y. Tsay, and C. Hwang, "Numerical computation of cross-covariance functionals for linear systems with multiple time delays," J. Chin. Inst. Eng., vol. 21, no. 4, pp. 409-423, 1998.
19. A. Talbot, "The evaluation of integrals of products of linear system responses - Part II: Continued-fraction methods," Quart. J. Mech. Appl. Math., pt. 4, vol. XII, pp. 504-520, 1959.