Billal Lekdim

This paper examines the well-posedness and adaptive stabilization of a satellite vibration caused by internal disturbances. The structure of the satellite is made up of two flexible, symmetrical wings that are connected to a central body. The wings are modeled as transmission Euler-Bernoulli beams with dynamic boundary conditions. We design high-gain adaptive regulators by measuring velocity feedback at the central body to quickly dampen vibrations. We demonstrate an exponential decay result for the system employing the multiplier method. The theoretical results are supported by a numerical simulation.

In this paper, we investigate the boundary control of flexible mechanical systems characterized by bending deformation, torsion deformation, and distributed delay. We establish the existence of solutions using the Faedo- Galerkin approach along with energy estimates. Under appropriate assumptions on the delay weight and the proposed control, we demonstrate the exponential stability of the solution via the Lyapunov method.

This research investigates a coupled wave system where the second equation is influenced by viscoelastic damping and is subject to Dirichlet boundary conditions on the interval (0, 1). For a broad class of relaxation functions and within a general framework, we establish the global existence of solutions using the Faedo-Galerkin method. In addition, we derive general decay estimates by applying Lyapunov?s method and employing certain convexity arguments.

In this paper, we investigated the vibration control of a satellite with two symmetric flexible panels attached with center body. The panels are modeled as transmission Euler-Bernoulli beam. We have proved the well-posedness by using semigroup theory. By applying a control force at the center body of the spacecraft, we established exponential decay result using the multiplier method. The theory is illustrated by a numerical example.

In this work, we consider the thermoelastic system with a nonlinear distributed delay. Under appropriate hypothesis on the weight function of the delay we prove well-posedness by using the Feado- Galerkin method. Also we establish an exponential decay result by introducing a suitable Lyapunov functional.