Boundary Control of a Non-Linear String

Boundary Control of Vibration and Noise in Distributed Parameter Systems: An Overview

“…We first observed the use of this term in [39]; however, we have since noted that other boundary control work often makes use of a similar term during the stability analysis (e.g. [6,18]). …”

Finite element approximation of the nonlinear Kirchhoff string with boundary control

“…For the details of the stabilization results of the nonlinear Kirchhoff string with linear or nonlinear feedback boundary control, please refer to [14,18]. The purpose of this work is to give a finite element approximation analysis of the closed-loop system (4)-(5).…”

“…The control input u in equation (3) is commonly known as the boundary control (Shahruz and Krishna, 1996). The measurement output of the system is y t (1, t).…”

“…On the other hand, the stabilization and convergence of Kirchhoff strings under external control is also an important subject for control practice of mechanical systems. The stabilization problem with boundary velocity feedback is studied by [14]. In the literature, a linear boundary velocity feedback control law is proposed and it is shown that the system under the proposed control law is exponentially stable by constructing an energy-like function, which is motivated by the spirit of the Lyapunov direct method.…”

Boundary position feedback control of Kirchhoff's non‐linear strings

“…On the other hands, the boundary stabilization of non-linear strings was investigated in References [11,12], where the boundary velocity feedback is used.…”