On partial stabilization of nonlinear autonomous systems: Sufficient conditions and examples

The problem of partial stabilization is considered for autonomous affine control system. The result on sufficient condition for partial stabilizability is proved, provided that open-loop system admits Lyapunov function with nonpositive lower bounds of derivatives. The result proposed is applied for solving the problem of single-axis stabilization of a rigid body. Two cases are considered. In the first case the control is implemented by jet engines, while in the second one the satellite is controlled by means of moving masses (flywheels). The explicit expressions of stabilizing feedback laws are given.