The sampled-data boundary control problem for a longitudinal flexible bar is formulated as a linear discrete-time control problem in an infinite-dimensional state space. With zero-order-hold applied to the control channel, the system is lifted into an infinite sequence of constant control problems. The finite-dimensional approximation of the discrete-time system is controllable-observable if the sampling period satisfies some inequality constraints, which are related to the associated eigenvalues.

1.
Zauderer, E. 1989, Partial Differential Equations of Applied Mathematics, Wiley-Interscience, New York.
2.
Rao, S. S., 1990, Mechanical Vibrations, Addison Wesley, New York.
3.
Drakunov
,
S.
, and
Utkin
,
V.
,
1992
, “
Sliding Mode Control in Dynamic Systems
,”
Int. J. Control
,
55
, No.
4
, pp.
1029
1037
.
4.
Kreyszig, E., 1979, Advanced Engineering Mathematics, Wiley, New York.
5.
Wallace, P. R., 1972, Mathematical Analysis of Physical Problems, Dover, New York.
6.
Lindfield, G., and Penny, J., 1995, Numerical Methods Using MATLAB, Ellis Horwood, New York.
You do not currently have access to this content.