Abstract:

An approach to stabilize a family of nonlinear systems via feedback nonlinearization is presented. A dummy output mapping is constructed so that the zero dynamics are made asymptotically stable and the system is of relative degree{1,…,1};then a group of controllers are designed that guarantee the exponential attractivity of the zeroing output manifold. Using tools in nonlinear H ∞ control theory, it is shown that under mild conditions, the resulting closed loop system is locally asymptotically stable. Finally, these results are used to the attitude control problem for a rigid body to design detumbling controllers that only require knowledge of relative value of the system inertial parameters. This technique seems attractive in that, to a certain extent, it may lessen the need of precise system knowledge required by the feedback linearization technique.

Key words: nonlinear systems, geometr ic approach, attitude contr ol