Andreev, A. S. Lyapunov functions method in control problems. (Russian. English summary) Zbl 1299.34210 Zh. Sredn. Mat. Obshch. 12, No. 4, 64-73 (2010). The stabilization of the trivial solution \(x=0\) for the system of differential equations \[ \dot { x}={ X}(t,{ x},{ u}),\;\;{ X}(t,{ 0},{ 0})\equiv { 0} \] is solved by comparison method and vector Lyapunov functions. The results are applied to the problem of motion control and to the stabilization of the inverted simple pendulum. Reviewer: Pavel A. Shamanaev (Saransk) MSC: 34H05 Control problems involving ordinary differential equations 93D30 Lyapunov and storage functions 34D20 Stability of solutions to ordinary differential equations Keywords:vector Lyapunov function; comparison method; limiting equations; stabilization; synthesis of control on the finite time interval PDFBibTeX XMLCite \textit{A. S. Andreev}, Zh. Sredn. Mat. Obshch. 12, No. 4, 64--73 (2010; Zbl 1299.34210)