Stabilization of a rigid body in a viscous incompressible fluid

Abstract

This paper addresses the problem of global asymptotic and local exponential stabilization of a rigid body inside a viscous incompressible fluid described by Navier–Stokes equations within a bounded domain in three dimensional space provided that there is no collision between the rigid body and the boundary of the fluid domain. Due to consideration of less regular initial values of the fluid velocity, the forces and moments induced by the fluid on the rigid body are not able to bound. Therefore, the paper handles “fluid work and fluid power” on the rigid body in stability and convergence analysis of the closed-loop system. The control design ensures global asymptotic and local exponential stability of the rigid body while the initial fluid velocity is not required to be small and regular but only under no collision between the rigid body and the boundary of the fluid domain.