ROBUSTNESS OF BOUNDARY CONTROL OF DAMPED WAVE EQUATIONS WITH LARGE DELAYS AT BOUNDARY MEASUREMENT

Abstract The Smith predictor is applied to the boundary control of damped wave equations with large delays at the boundary measurement. The instability problem due to large delays is solved and the scheme is proved to be robust against a small difference between the assumed delay and the actual delay.

[1]  O Wan-tang.  On the Stability of a Flexible Beam with a Tip Mass , 2007 .

[2]  O. Morgul.  Stabilization and disturbance rejection for the wave equation , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[3]  R. Datko,et al.  Two examples of ill-posedness with respect to small time delays in stabilized elastic systems , 1993, IEEE Trans. Autom. Control..

[4]  Omer Morgiil,et al.  On the Stabilization and Stability Robustness Against Small Delays of Some Damped Wave Equations , 1995 .

[5]  Hartmut Logemann,et al.  PDEs with Distributed Control and Delay in the Loop: Transfer Function Poles, Exponential Modes and Robustness of Stability , 1998, Eur. J. Control.

[6]  Yury Orlov,et al.  On minmax filtering over discrete-continuous observations , 1995, IEEE Trans. Autom. Control..

[7]  Ömer Morgül.  An exponential stability result for the wave equation , 2002, Autom..

[8]  O Smith,et al.  CLOSER CONTROL OF LOOPS WITH DEAD TIME , 1957 .

[9]  Ömer Morgül.  Stabilization and disturbance rejection for the beam equation , 2001, IEEE Trans. Autom. Control..

[10]  Michael P. Polis,et al.  An example on the effect of time delays in boundary feedback stabilization of wave equations , 1986 .

[11]  Ömer Morgül,et al.  ON THE BOUNDARY CONTROL OF BEAM EQUATION , 2002 .

[12]  Kok Kiong Tan,et al.  Finite-Spectrum Assignment for Time-Delay Systems , 1998 .

[13]  Hartmut Logemann,et al.  Conditions for Robustness and Nonrobustness of theStability of Feedback Systems with Respect to Small Delays inthe Feedback Loop , 1996 .

[14]  J. Lagnese,et al.  An example of the effect of time delays in boundary feedback stabilization of wave equations , 1985, 1985 24th IEEE Conference on Decision and Control.

[15]  William S. Levine,et al.  The Control Handbook , 2010 .

[16]  Ö. Morgül,et al.  On the Stabilization of a Flexible Beam with a Tip Mass , 1998 .

[17]  A. Krall,et al.  Modeling stabilization and control of serially connected beams , 1987 .

[18]  Bao-Zhu Guo,et al.  Riesz Basis Approach to the Stabilization of a Flexible Beam with a Tip Mass , 2000, SIAM J. Control. Optim..

[19]  C. SIAMJ.,et al.  RIESZ BASIS PROPERTY AND EXPONENTIAL STABILITY OF CONTROLLED EULER–BERNOULLI BEAM EQUATIONS WITH VARIABLE COEFFICIENTS∗ , 2002 .

[20]  K. S. Narendra,et al.  Stabilization and Disturbance Rejection for the Wave Equation , 1998 .