TY - JOUR
AU1 - Karafyllis, Iasson
AU2 - Krstic, Miroslav
AB - This paper is devoted to the study of the robustness properties of the 1-D wave equation for an elastic vibrating string under four different damping mechanisms that are usually neglected in the study of the wave equation: (i) friction with the surrounding medium of the string (or viscous damping), (ii) thermoelastic phenomena (or thermal damping), (iii) internal friction of the string (or Kelvin-Voigt damping), and (iv) friction at the free end of the string (the so-called passive damper). The passive damper is also the simplest boundary feedback law that guarantees exponential stability for the string. We study robustness with respect to distributed inputs and boundary disturbances in the context of Input-to-State Stability (ISS). By constructing appropriate ISS Lyapunov functionals, we prove the ISS property expressed in various spatial norms.
TI - ISS-based robustness to various neglected damping mechanisms for the 1-D wave PDE
JF - Mathematics of Control Signals and Systems
DO - 10.1007/s00498-023-00353-6
DA - 2023-12-01
UR - https://www.deepdyve.com/lp/springer-journals/iss-based-robustness-to-various-neglected-damping-mechanisms-for-the-1-Gc3evwiB9q
SP - 741
EP - 779
VL - 35
IS - 4
DP - DeepDyve
ER -