Robustness of boundary control of damped wave equations with large delays at boundary measurement

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 16, Issue , 2005, Pages 60-64

  Liang, Jinsong ^a   Zhang, Weiwei ^b   Chen, YangQuan ^a  

^a Utah State University   (United States)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Damped wave equation; Delay; Robust boundary control; Smith predictor

Indexed keywords

BOUNDARY CONTROLS; BOUNDARY MEASUREMENTS; DAMPED WAVE EQUATIONS; DELAY; INSTABILITY PROBLEMS; LARGE DELAYS; SMITH PREDICTORS;

WAVE EQUATIONS;

EID: 79960710396     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20050703-6-cz-1902.00954     Document Type: Conference Paper

References (17)

1. Chen, G. (1979). Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain. J. Math. Pure. Appl. 58, 249-273.
2. Chen, G., M. C. Delfour, A. M. Krall and G. Payre (1987). Modelling, stabilization and control of serially connected beams. SIAM J. Contr. Optimiz. 25, 526-546.
3. Conrad, Francis and Ömer Morgül (1998). On the stability of a flexible beam with a tip mass. SIAM journal of control and optimization 36(6), 1962-1986.
4. Datko, R. (1993). Two examples of ill-posedness with respect to small time delays in stabilized elastic systems. IEEE Transactions on automatic control 38(1), 163-166.
5. Datko, R., J. Lagnese and M. P. Polis (1986). An example on the effect of time delays in boundary feedback stabilization of wave equations. SIAM J. Control Optim. 24, 152- 156.
6. Guo, Bao-Zhu (2001). Riesz basis approach to the stabilization of a flexible beam with a tip mass. SIAM J. Control Optim. 39(6), 1736- 1747.
7. Guo, Bao-Zhu (2002). Riesz basis property and exponential stability of controlled eulerbernoulli beam equations with variable coefficients. SIAM J. Control Optim. 40(6), 1905- 1923.
8. Levine, W., Ed.) (1996). The Control handbook. pp. 224-237. CRC Press.
9. Logemann, H. and R. Rebarber (1998). PDEs with distributed control and delay in the loop: transfer function poles, exponential modes and robustness of stability. European Journal of Control 4(4), 333-344.
10. Logemann, Hartmut, Richard Rebarber and George Weiss (1996). Conditions for robustness and nonrobustness of the stability of feedback systems with respect to small delays in the feedback loop. SIAM J. Control and Optimimization 34(2), 572-600.
11. Morgül, Ömer (1995). On the stabilization and stability robustness against small delays of some damped wave equations. IEEE Transactions on Automatic Control 40(9), 1626- 1623.
12. Morgül, Ömer (1998). Stabilization and disturbance rejection for the wave equation. IEEE Transactions on Automatic Control 43(1), 89-95.
13. Morgül, Ömer (2001). Stabilization and disturbance rejection for the beam equation. IEEE Transactions on Automatic Control 46(12), 1913-1918.
14. Morgül, Ömer (2002a). An exponential stability result for the wave equation. Automatica 38, 731-735.
15. Morgül, Ömer (2002b). On the boundary control of beam equation. In: Proc. of the 15-th IFAC World Congress on Automatic Control.
16. Smith, O. J. M. (1957). Closer control of loops with dead time. Chem. Eng. Progress 53(5), 217-219.
17. Wang, Qing-Guo, Tong Heng Lee and Kok Kiong Tan (1999). Finite Spectrum Assignment for Time-delay Systems. Spring Verlag.