Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 48, Issue 9, Pages 1496-1508Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2003.816963
Keywords
feedback law; Lie groups; nonlinear systems; stabilization
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A general control design approach for the stabilization of controllable driftless nonlinear systems on finite dimensional Lie groups is presented. The approach is based on the concept of bounded transverse functions, the existence of which is equivalent to the system's controllability. Its outcome is the practical stabilization of any trajectory, i.e., not necessarily a solution of the control system, in the state-space. The possibility of applying the approach to an arbitrary controllable smooth driftless system follows in turn from the fact that any controllable homogeneous approximation of this system can be lifted (via a dynamic extension) to a system on a Lie group. Illustrative examples are given.
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