2021/12/21 by Karafyllis, Iasson, Krstic, Miroslav
#Analysis of PDEs (math.AP) #Classical Physics (physics.class-ph) #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2112.11287
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.