Construction of stabilizing feedback law by means of control Lyapunov function with respect to a part of the variables. (Russian) Zbl 0966.93092

Zuyev, A. L.

Tr. Inst. Prikl. Mat. Mekh. 4, 70-76 (1999).

The problem of partial stabilization by means of a static time-invariant feedback law is investigated. The class of admissible feedback laws under consideration consists of locally bounded measurable functions, and the solutions of the closed-loop system are defined in the sense of A. F. Filippov. The notion of control Lyapunov function with respect to a part of the variables is introduced. It is proved that if the above function exists, then the control system is stabilizable with respect to a part of the variables. This result extends Artstein’s theorem for the case of partial stabilization. The constructive feedback design is proposed for affine control system provided that there exists a control Lyapunov function with respect to a part of the variables. The obtained feedback law is proved to be continuous under some additional assumptions on the Lyapunov function.

Reviewer: Alexander Mikhailovich Kovalev (Donetsk)

MSC:

93D15	Stabilization of systems by feedback
93D30	Lyapunov and storage functions

Keywords:

partial stabilization; control Lyapunov function; solution in the sense of A. F. Filippov; Artstein’s theorem