A Sampled-Data Formulation for Boundary Control of a Longitudinal Elastic Bar

Abstract

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.