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Observability for port-Hamiltonian systems | IEEE Conference Publication | IEEE Xplore

Observability for port-Hamiltonian systems


Abstract:

The class of port-Hamiltonian systems incorporates many physical models, such as mechanical systems in the finite-dimensional case and wave and beam equations in the infi...Show More

Abstract:

The class of port-Hamiltonian systems incorporates many physical models, such as mechanical systems in the finite-dimensional case and wave and beam equations in the infinite-dimensional case. In this paper we study a subclass of linear first order port-Hamiltonian systems. In [3], it is shown that these systems are exactly observable when the energy is not dissipated internally and when sufficient observations are made at the boundary. In this article we study the observability properties for these systems when internal dissipation of energy is possible. We cannot show the exact observability, but we do show that the Hautus test is satisfied. In general, the Hautus test is weaker than exact observability, but stronger than approximate observability. Hence we conclude that these systems are approximately observable.
Date of Conference: 29 June 2021 - 02 July 2021
Date Added to IEEE Xplore: 03 January 2022
ISBN Information:
Conference Location: Delft, Netherlands

I. Introduction

In this paper we investigate the exact observability of port-Hamiltonian systems of the form \begin{align*}& \frac{{\partial x}}{{\partial t}}(\zeta ,t) = \left({{P_1}\frac{\partial }{{\partial \zeta }} + {G_0}}\right)({\mathcal{H}}(\zeta )x(\zeta ,t)), \\ & x(\zeta ,0) = {x_0}(\zeta ), \\ & 0 = \left[ {{W_{B,1}}\quad {W_{B,0}}} \right]\left[ {\begin{array}{c} {({\mathcal{H}}x)(1,t)} \\ {({\mathcal{H}}x)(0,t)} \end{array}} \right], \\ & y(t) = \left[ {{W_{C,1}}\quad {W_{C,0}}} \right]\left[ {\begin{array}{c} {({\mathcal{H}}x)(1,t)} \\ {({\mathcal{H}}x)(0,t)} \end{array}} \right],\end{align*} where ζ ∈ [0, 1] and t ≥ 0. We refer to Section III for the precise assumptions on P1, G0, [WB,1 WB,0], [WC,1 WC,0] and .

References

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