Publication

Stability conditions for infinite networks of nonlinear systems and their application for stabilization

Dashkovskiy, S. & Pavlichkov, S., Feb-2020, In : Automatica. 112, 12 p., 108643.

Research output: Contribution to journalArticleAcademicpeer-review

APA

Dashkovskiy, S., & Pavlichkov, S. (2020). Stability conditions for infinite networks of nonlinear systems and their application for stabilization. Automatica, 112, [108643]. https://doi.org/10.1016/j.automatica.2019.108643

Author

Dashkovskiy, Sergey ; Pavlichkov, Svyatoslav. / Stability conditions for infinite networks of nonlinear systems and their application for stabilization. In: Automatica. 2020 ; Vol. 112.

Harvard

Dashkovskiy, S & Pavlichkov, S 2020, 'Stability conditions for infinite networks of nonlinear systems and their application for stabilization', Automatica, vol. 112, 108643. https://doi.org/10.1016/j.automatica.2019.108643

Standard

Stability conditions for infinite networks of nonlinear systems and their application for stabilization. / Dashkovskiy, Sergey; Pavlichkov, Svyatoslav.

In: Automatica, Vol. 112, 108643, 02.2020.

Research output: Contribution to journalArticleAcademicpeer-review

Vancouver

Dashkovskiy S, Pavlichkov S. Stability conditions for infinite networks of nonlinear systems and their application for stabilization. Automatica. 2020 Feb;112. 108643. https://doi.org/10.1016/j.automatica.2019.108643


BibTeX

@article{cd2233dfc81741b8820e3ec92aa1b93e,
title = "Stability conditions for infinite networks of nonlinear systems and their application for stabilization",
abstract = "We introduce a new concept of l(infinity)-input-to-state stability for infinite networks composed of a countable set of interconnected nonlinear subsystems of ordinary differential equations. We suppose that the entire state vector is an element of l(infinity) and each subsystem is input-to-state stable whereas the dimension of its entire disturbance input including possible interconnections with other subsystems is finite. Our first main result provides conditions for l(infinity)-input-to-state stability of such infinite-dimensional networks. In our second main result, we solve the problem of decentralized l(infinity)-ISS stabilization for such networks composed of interconnected lower-triangular form subsystems with uncontrollable linearization. To apply our first main result and obtain the second one, we construct a feedback for each individual agent, which satisfies our new stability conditions. This yields the stabilization of the entire network. Our design is also new for finite networks and this can be considered as an important special case. (C) 2019 Elsevier Ltd. All rights reserved.",
keywords = "Nonlinear systems, Input-to-state stability, Small gain theorems, Infinite networks, Decentralized control, SMALL-GAIN THEOREM, TO-STATE STABILITY, DISTRIBUTED CONTROL, STRING STABILITY, CONSTRUCTION, IISS",
author = "Sergey Dashkovskiy and Svyatoslav Pavlichkov",
year = "2020",
month = "2",
doi = "10.1016/j.automatica.2019.108643",
language = "English",
volume = "112",
journal = "Automatica",
issn = "1873-2836",
publisher = "PERGAMON-ELSEVIER SCIENCE LTD",

}

RIS

TY - JOUR

T1 - Stability conditions for infinite networks of nonlinear systems and their application for stabilization

AU - Dashkovskiy, Sergey

AU - Pavlichkov, Svyatoslav

PY - 2020/2

Y1 - 2020/2

N2 - We introduce a new concept of l(infinity)-input-to-state stability for infinite networks composed of a countable set of interconnected nonlinear subsystems of ordinary differential equations. We suppose that the entire state vector is an element of l(infinity) and each subsystem is input-to-state stable whereas the dimension of its entire disturbance input including possible interconnections with other subsystems is finite. Our first main result provides conditions for l(infinity)-input-to-state stability of such infinite-dimensional networks. In our second main result, we solve the problem of decentralized l(infinity)-ISS stabilization for such networks composed of interconnected lower-triangular form subsystems with uncontrollable linearization. To apply our first main result and obtain the second one, we construct a feedback for each individual agent, which satisfies our new stability conditions. This yields the stabilization of the entire network. Our design is also new for finite networks and this can be considered as an important special case. (C) 2019 Elsevier Ltd. All rights reserved.

AB - We introduce a new concept of l(infinity)-input-to-state stability for infinite networks composed of a countable set of interconnected nonlinear subsystems of ordinary differential equations. We suppose that the entire state vector is an element of l(infinity) and each subsystem is input-to-state stable whereas the dimension of its entire disturbance input including possible interconnections with other subsystems is finite. Our first main result provides conditions for l(infinity)-input-to-state stability of such infinite-dimensional networks. In our second main result, we solve the problem of decentralized l(infinity)-ISS stabilization for such networks composed of interconnected lower-triangular form subsystems with uncontrollable linearization. To apply our first main result and obtain the second one, we construct a feedback for each individual agent, which satisfies our new stability conditions. This yields the stabilization of the entire network. Our design is also new for finite networks and this can be considered as an important special case. (C) 2019 Elsevier Ltd. All rights reserved.

KW - Nonlinear systems

KW - Input-to-state stability

KW - Small gain theorems

KW - Infinite networks

KW - Decentralized control

KW - SMALL-GAIN THEOREM

KW - TO-STATE STABILITY

KW - DISTRIBUTED CONTROL

KW - STRING STABILITY

KW - CONSTRUCTION

KW - IISS

U2 - 10.1016/j.automatica.2019.108643

DO - 10.1016/j.automatica.2019.108643

M3 - Article

VL - 112

JO - Automatica

JF - Automatica

SN - 1873-2836

M1 - 108643

ER -

ID: 128588313