Stability analysis and synthesis of stabilizing controls for a class of nonlinear mechanical systems

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Stability analysis and synthesis of stabilizing controls for a class of nonlinear mechanical systems. / Aleksandrov, A. Yu.

In: Nonlinear Dynamics, Vol. 100, No. 4, 01.06.2020, p. 3109-3119.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{8abcfc15f443429f9684060290e21570,

title = "Stability analysis and synthesis of stabilizing controls for a class of nonlinear mechanical systems",

abstract = "This paper is concerned with the problems of stability and stabilization for a class of nonlinear mechanical systems. It is assumed that considered systems are under the action of linear gyroscopic forces, nonlinear homogeneous positional forces and nonlinear homogeneous dissipative forces of positional–viscous friction. An approach to strict Lyapunov functions construction for such systems is proposed. With the aid of these functions, sufficient conditions of the asymptotic stability and estimates of the convergence rate of solutions are found. Moreover, systems with delay in the positional forces are studied, and new delay-independent stability conditions are derived. The obtained results are used for developing new approaches to the synthesis of stabilizing controls with delay in feedback law.",

keywords = "Asymptotic stability, Decomposition, Delay, Lyapunov function, Nonlinear mechanical system, Stabilization",

author = "Aleksandrov, {A. Yu}",

year = "2020",

month = jun,

day = "1",

doi = "10.1007/s11071-020-05709-0",

language = "English",

volume = "100",

pages = "3109--3119",

journal = "Nonlinear Dynamics",

issn = "0924-090X",

publisher = "Springer Nature",

number = "4",

}

RIS

TY - JOUR

T1 - Stability analysis and synthesis of stabilizing controls for a class of nonlinear mechanical systems

AU - Aleksandrov, A. Yu

PY - 2020/6/1

Y1 - 2020/6/1

N2 - This paper is concerned with the problems of stability and stabilization for a class of nonlinear mechanical systems. It is assumed that considered systems are under the action of linear gyroscopic forces, nonlinear homogeneous positional forces and nonlinear homogeneous dissipative forces of positional–viscous friction. An approach to strict Lyapunov functions construction for such systems is proposed. With the aid of these functions, sufficient conditions of the asymptotic stability and estimates of the convergence rate of solutions are found. Moreover, systems with delay in the positional forces are studied, and new delay-independent stability conditions are derived. The obtained results are used for developing new approaches to the synthesis of stabilizing controls with delay in feedback law.

AB - This paper is concerned with the problems of stability and stabilization for a class of nonlinear mechanical systems. It is assumed that considered systems are under the action of linear gyroscopic forces, nonlinear homogeneous positional forces and nonlinear homogeneous dissipative forces of positional–viscous friction. An approach to strict Lyapunov functions construction for such systems is proposed. With the aid of these functions, sufficient conditions of the asymptotic stability and estimates of the convergence rate of solutions are found. Moreover, systems with delay in the positional forces are studied, and new delay-independent stability conditions are derived. The obtained results are used for developing new approaches to the synthesis of stabilizing controls with delay in feedback law.

KW - Asymptotic stability

KW - Decomposition

KW - Delay

KW - Lyapunov function

KW - Nonlinear mechanical system

KW - Stabilization

UR - http://www.scopus.com/inward/record.url?scp=85086125522&partnerID=8YFLogxK

U2 - 10.1007/s11071-020-05709-0

DO - 10.1007/s11071-020-05709-0

M3 - Article

AN - SCOPUS:85086125522

VL - 100

SP - 3109

EP - 3119

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 4

ER -

ID: 61006632