Motion planning and partial stabilization of infinite-dimensional systems

The paper deals with issues of mathematical modeling of hybrid mechanical systems consisting of rigid and deformable bodies. Under some assumptions the motion of such objects can be described by a system of ordinary differential equations evolving in a Banach space. A sufficient condition for partial asymptotic stability of autonomous nonlinear systems in Banach spaces is obtained. With the help of this result a technique for hybrid controller design is proposed. The above outcomes are applied for solving the stabilization problem of a rigid body with flexible elements. In conclusion, the results of numerical simulation are given