Uniform Stabilization of a Hybrid System of Elasticity: Riesz Basis Approach

Boundary stabilization of an overhead crane with beam model

“…where α > 0, β > 0, and K = 0. When I m = 0, the uniform stabilization of the hybrid system is obtained in [1] by means of a feedback law taking into account only the position and the velocity of the platform. i.e.…”

“…In section 2, the asymptotic expressions of eigenvalues and eigenfunctions are derived. In Section 3, we show that there is a sequence of generalized eigenfunctions of system (1), which forms a Riesz basis for the state Hilbert space and the exponential stability of the system is proved. Numerical simulation of the distribution of eigenvalues is presented in the first part of section 4 after relating the stability of the system to a finite dimensional eigenvalue problem and the effectiveness of the control is presented in the second part of section 4.…”