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Constant-sign Lyapunov functionals in stability problem for functional differential equation. (Russian, English) Zbl 1164.34035

Prikl. Mat. Mekh. 71, No. 3, 377-388 (2007); translation in J. Appl. Math. Mech. 71, No. 3, 339-350 (2007).
The author proposes to study the stability of zero solutions of non-autonomous functional differential delay-type equations by means of limiting equations and sign-definite Lyapunov functionals with sign-constant derivative. Also, partial cases are considered when the Lyapunov functional and its derivative do not explicitly depend on time, as well as the case of an almost periodic equation. As examples, a problem on the stabilization of a pendulum in the unstable upper state and a problem on the stabilization of a rotational motion of a rigid body are solved.

MSC:

34K20 Stability theory of functional-differential equations
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
93D15 Stabilization of systems by feedback
70K20 Stability for nonlinear problems in mechanics
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References:

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