Application of the Lyapunov function with fixed sign derivative in problems of partial stabilization. (Russian) Zbl 1047.70600

It is known that any controllable linear system is stabilizable. But, in general, such statement is incorrect even for affine control systems. One of the effective tools for stability investigation of nonlinear control systems is the control Lyapunov functions method, suggested in Artstein’s papers. At the same time many mechanical control systems have the first integral and therefore cannot be stabilizable on all variables. In the paper the feedback law by means of known control Lyapunov function with respect to a part of the variables for nonlinear control system is obtained. The theorem of existence of a continuous feedback ensuring the stabilization with respect to a part of variables is proved. The obtained results are applied to the problem of the uniaxial stabilization of a rigid body. The feedback, stabilizing rotation of a rigid body around the specific axis, is constructed.


70E50 Stability problems in rigid body dynamics
93B52 Feedback control