Galerkin Approximations for Stability of Delay Differential Equations with Time Periodic Coefficients

Journal of Computational and Nonlinear Dynamics

Volumn 10, Issue 2, 2015, Pages

  Sadath, Anwar ^a   Vyasarayani, C P ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY HYDERABAD   (India)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; GALERKIN METHODS; NUMERICAL METHODS; STABILITY;

DELAY DIFFERENTIAL EQUATIONS; GALERKIN APPROXIMATIONS; GALERKIN LEAST SQUARES; PARTIAL DIFFERENTIAL EQUATIONS (PDE); SHIFTED LEGENDRE POLYNOMIALS; SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS; TIME PERIODIC COEFFICIENTS; TIME-PERIODIC BOUNDARY CONDITIONS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 84940473580     PISSN: 15551415     EISSN: 15551423     Source Type: Journal    
DOI: 10.1115/1.4026989     Document Type: Article

References (18)

1. Insperger, T., and Stepan, G., 2002, "Semi-Discretization Method for Delayed Systems," Int. J. Numer. Methods Eng., 55(5), pp. 503-518.
2. Insperger, T., and Stepan, G., 2004, "Updated Semi-Discretization Method for Periodic Delay-Differential Equations With Discrete Delay," Int. J. Numer. Methods Eng., 61(1), pp. 117-141.
3. Elbeyli, O., and Sun, J. Q., 2004, "On the Semi-Discretization Method for Feedback Control Design of Linear Systems With Time Delay," J. Sound Vib., 273(1), pp. 429-440.
4. Garg, N. K., Mann, B. P., Kim, N. H., and Kurdi, M. H., 2007, "Stability of a Time-Delayed System With Parametric Excitation," ASME J. Dyn. Syst. Measure. Control, 129, pp. 125-135.
5. Butcher, E. A., Bobrenkov, O. A., Bueler, E., and Nindujarala, P., 2009, "Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels," ASME J. Comput. Nonlinear Dyn., 4, p. 031003.
6. Khasawneh, F. A., Mann, B. P., and Butcher, E. A., 2011, "A Multi-Interval Chebyshev Collocation Approach for the Stability of Periodic Delay Systems With Discontinuities," Commun. Nonlinear Sci. Numer. Simul., 16(11), pp. 4408-4421.
7. Sun, J. Q., 2009, "A Method of Continuous Time Approximation of Delayed Dynamical Systems," Commun. Nonlinear Sci. Numer. Simul., 14(4), pp. 998-1007.
8. Sun, J. Q., and Song, B., 2009, "Control Studies of Time-Delayed Dynamical Systems With the Method of Continuous Time Approximation," Commun. Nonlinear Sci. Numer. Simul., 14(11), pp. 3933-3944.
9. Breda, D., Maset, S., and Vermiglio, R., 2005, "Pseudospectral Differencing Methods for Characteristic Roots of Delay Differential Equations," SIAM J. Sci. Comput., 27(2), pp. 482-495.
10. Bobrenkov, O. A., Nazari, M., and Butcher, E. A., 2012, "Response and Stability Analysis of Periodic Delayed Systems With Discontinuous Distributed Delay," ASME J. Comput. Nonlinear Dyn., 7(3), p. 031010.
11. Bobrenkov, O. A., Butcher, E. A., and Mann, B. P., 2013, "Application of the Liapunov-Floquet Transformation to Differential Equations With Time Delay and Periodic Coefficients," J. Vib. Control, 19(4), pp. 521-537.
12. Butcher, E. A., and Bobrenkov, O. A., 2011, "On the Chebyshev Spectral Continuous Time Approximation for Constant and Periodic Delay Differential Equations," Commun. Nonlinear Sci. Numer. Simul., 16(3), pp. 1541-1554.
13. Bellen, A., and Maset, S., 2000, "Numerical Solution of Constant Coefficient Linear Delay Differential Equations As Abstract Cauchy Problems," Numer. Math., 84(3), pp. 351-374.
14. Wahi, P., and Chatterjee, A., 2005, "Galerkin Projections for Delay Differential Equations," ASME J. Dyn. Syst. Measure. Control, 127(1), pp. 80-87.
15. Vyasarayani, C. P., 2012, "Galerkin Approximations for Higher Order Delay Differential Equations," ASME J. Comput. Nonlinear Dyn., 7(3), p. 031004.
16. Luenberger, D. G., 2003, Linear and Nonlinear Programming, Springer, Berlin.
17. Segalman, D. J., and Butcher, E. A., 2000, "Suppression of Regenerative Chatter Via Impedance Modulation," J. Vib. Control, 6(2), pp. 243-256.
18. Nayfeh, A. H., and Mook, D. T., 2008, Nonlinear Oscillations, Wiley, New York.