Stabilization of the motions of controlled mechanical systems by a regulator with delay

Pavlikov, S. V.

doi:10.1134/s1064562407010462

Cited by 5 publications

(2 citation statements)

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“…It is worth noting that systems with distributed delays arise in traffic flow models, in network control systems, in PID controller design and in other engineering applications [Bullo, Cortes and Martinez, 2009;Gu, Kharitonov and Chen, 2003;Fridman, 2014;Solomon and Fridman, 2013]. Some conditions of stability and stabilization of mechanical systems with distributed delays were obtained, for instance, in [Anan'evskii and Kolmanovskii, 1989;Pavlikov, 2007]. Let us show that the approach proposed in the previous section can be used for the stability analysis of the system (9), as well.…”

Section: A System With Distributed Delaymentioning

confidence: 99%

Stability analysis of gyroscopic systems with discrete and distributed delays

Aleksandrov

Semenov

Zhan

2019

CAP

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This paper provides stability analysis results for a linear mechanical system with a large parameter at the vector of gyroscopic forces and with delay in positional forces. Both cases of discrete and distributed delay are studied. Using the decomposition method and Lyapunov-Krasovskii functionals, conditions are found under which delay does not disturb the asymptotic stability of the considered system. The effectiveness of the obtained results is illustrated by a simulation example.

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Section: A System With Distributed Delaymentioning

confidence: 99%

Stability analysis of gyroscopic systems with discrete and distributed delays

Aleksandrov

Semenov

Zhan

2019

CAP

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“…This approach is well developed for the case in which the forces applied to the system and the control to be constructed are linear [16][17][18][19][20][21]. However, note that the asymptotic stability in linear systems occurs only for certain delay values.…”

Section: Synthesis Of Stabilizing Controlsmentioning

confidence: 99%

On the asymptotic stability of equilibria of nonlinear mechanical systems with delay

Aleksandrov

Zhabko

2013

Diff Equat

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We consider some classes of nonlinear mechanical systems with retarded argument. It is assumed that, in the absence of delay, the systems in question have asymptotically stable equilibria. We analyze how the delay affects the stability of these equilibria. The Lyapunov function method and Razumikhin's approach are used to derive conditions under which asymptotic stability is preserved for arbitrary delay values. We suggest a method for stabilizing strongly nonlinear conservative systems by constructing a delay feedback control depending only on the generalized coordinates.

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On the attitude stabilization of a rigid body under control with distributed delay

Aleksandrov

Тихонов

2021

Mechanics Based Design of Structures and Machines

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Stabilization of the motions of controlled mechanical systems by a regulator with delay

Cited by 5 publications

References 0 publications

Stability analysis of gyroscopic systems with discrete and distributed delays

Stability analysis of gyroscopic systems with discrete and distributed delays

On the asymptotic stability of equilibria of nonlinear mechanical systems with delay

On the attitude stabilization of a rigid body under control with distributed delay

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