What is it about?
In the implementation of feedback-controls a delay can occur. We analyze the effect of this delay for wave-like systems with source terms: It turns out that the stabilizability of the system depends on the length: If the length is sufficiently small, the system can be stabilized exponentially fast. However, if the source term plays an important role in the system, stabilization becomes impossible if the length is too large.
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Why is it important?
Understanding the limits of a given feedback controler is important since for example it helps to assess the necessity of additional controlers for lage scale systems such as gas pipeline networks (as studied in the TRR 154). It is also an important result that a sufficiently regular time-delay does not prevent exponential stabilization, since in the use of digital controlers time-delay appears regularly.
Perspectives
It would be of high interest to show a similar result for networked system where the locations of the controlers are distributed in the graph of the network.
Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Read the Original
This page is a summary of: Boundary Stabilization of Quasi-linear Hyperbolic Systems with Varying Time-Delay, SIAM Journal on Control and Optimization, February 2025, Society for Industrial & Applied Mathematics (SIAM),
DOI: 10.1137/24m1648570.
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