Exact controllability of a system of coupled strings in parallel

Abstract

We consider a system of parallel identical strings coupled by distributed springs and dampers. It is shown that despite the distributed damping, there exists a branch of eigenvalues that is purely imaginary leading to sustained oscillations. It is also proved that when Dirichlet boundary controls are applied and the control time is greater than or equal to , where c is the wave speed, the system is exactly controllable in an appropriate state space.

Keywords:

• exact controllability
• wave equation
• moment problem
• Riesz basis
• non-harmonic Fourier series

AMS Subject Classifications::

• Primary: 93D05
• Secondary: 93B07