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Lyapunov functions method in control problems. (Russian. English summary) Zbl 1299.34210

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.

MSC:

34H05 Control problems involving ordinary differential equations
93D30 Lyapunov and storage functions
34D20 Stability of solutions to ordinary differential equations
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