IJCAS

In this paper, the problem of partial asymptotic stabilization of nonlinear control cascaded systems with integrators is considered. Unfortunately, many controllable control systems present an anomaly, which is the non complete stabilization via continuous pure-state feedback. This is due to Brockett necessary condition. In order to cope with this difficulty we propose in this work the partial asymptotic stabilization. For a given motion of a dynamical system, say the partial stabilization is the qualitative behavior of the y-component of the motion (i.e., the asymptotic stabilization of the motion with respect to y) and the z-component converges, relative to the initial vector In this work we present new results for the adding integrators for partial asymptotic stabilization. Two applications are given to illustrate our theoretical result. The first problem treated is the partial attitude control of the rigid spacecraft with two controls. The second problem treated is the partial orientation of the underactuated ship.

Keywords: Attitude stabilization, backstepping, linearization, Lyapunov-Malkin theorem, partial asymptotic stabilization, rigid spacecraft, ship.