Boundary feedback stabilization by piecewise constant time delay for the\n wave equation

2010/06/11 by Martin Gugat, Gugat, Martin, Marius Tucsnak +1
Computer Science · Engineering · Mathematics · #93B52 #93C20 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1006.2212

openalex publication_date 2010/06/11 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

For vibrating systems, a delay in the application of a feedback control can\ndestroy the stabilizing effect of the control. In this paper we consider a\nvibrating string that is fixed at one end and stabilized with a boundary\nfeedback with delay at the other end. We show that for certain feedback\nparameters the system is exponentially stable with constant delays of the form\n4L/c, 8L/c, 12L/c ... Moreover, we show that the system is exponentially stable\nwith piecewise constant delays that attain the values 4L/c and 8L/c.\n

Citations

• Nonharmonic Fourier series in the control theory of distributed parameter systems

Related

• Interior feedback stabilization of wave equations with dynamic boundary delay
• Feedback boundary stabilization of wave equations with interior delay
• On stability and stabilization of elastic systems by time-variant feedback
• Boundary stabilization of a one-dimensional wave equation by a switching\n time-delay: a theoretical and numerical study
• Existence and exponential stability of a damped wave equation with dynamic boundary conditions and a delay term