Exponential decay rate bound of one-dimensional distributed port-Hamiltonian systems with boundary dissipation
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Abstract
Distributed port-Hamiltonian systems with boundary damping and possible internal dissipation are considered. The multiplier method is used to show exponential decay Me <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−αt</sup> with an expression for M and α in terms of the system parameters. The exponential stability of port-Hamiltonian systems has been studied in the literature, but previous results did not provide an explicit bound on the decay rate. This result is illustrated by the boundary stabilization of a Timoshenko beam.
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