Boundary input-to-state stabilization of a damped Euler-Bernoulli beam in the presence of a state-delay

Hugo Lhachemi; Robert Shorten

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arXiv · 1912.01117

Boundary input-to-state stabilization of a damped Euler-Bernoulli beam in the presence of a state-delay

Hugo Lhachemi·Robert Shorten

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Abstract

This paper is concerned with the point torque boundary feedback stabilization of a damped Euler-Bernoulli beam model in the presence of a time-varying state-delay. First, a finite-dimensional truncated model is derived by spectral reduction. Then, for a given stabilizing state-feedback of the delay-free truncated model, an LMI-based sufficient condition on the maximum amplitude of the state-delay is employed to guarantee the stability of the closed-loop state-delayed truncated model. Second, we assess the exponential stability of the resulting closed-loop infinite-dimensional system under the assumption that the number of modes of the original infinite-dimensional system captured by the truncated model has been selected large enough. Finally, we consider in our control design the possible presence of a distributed perturbation, as well as additive boundary perturbations in the control inputs. In this case, we derive for the closed-loop system an exponential input-to-state estimate with fading memory of the distributed and boundary disturbances.

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BibTeX RIS

Hugo Lhachemi, Robert Shorten. 2019-12-02. Boundary input-to-state stabilization of a damped Euler-Bernoulli beam in the presence of a state-delay. https://arxiv.org/abs/1912.01117

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