Convergence to Periodic Regimes in Nonlinear Feedback Systems with a Strongly Convex Backlash

Igor G. Vladimirov; Ian R. Petersen

Convergence to Periodic Regimes in Nonlinear Feedback Systems with a Strongly Convex Backlash

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper considers a class of nonlinear systems consisting of a linear part with an external input and a nonlinear feedback with a backlash. Assuming that the latter is specified by a strongly convex set, we establish estimates for the Lyapunov exponents which quantify the rate of convergence of the system trajectories to a forced periodic regime when the input is a periodic function of time. These results employ enhanced dissipation inequalities for differential inclusions with strongly convex sets, which were used previously for the Moreau sweeping process.

Original language	English
Title of host publication	European Control Conference 2020, ECC 2020
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	71-76
Number of pages	6
ISBN (Electronic)	9783907144015
Publication status	Published - May 2020
Event	18th European Control Conference, ECC 2020 - Saint Petersburg, Russian Federation Duration: 12 May 2020 → 15 May 2020

Publication series

Name	European Control Conference 2020, ECC 2020

Conference

Conference	18th European Control Conference, ECC 2020
Country/Territory	Russian Federation
City	Saint Petersburg
Period	12/05/20 → 15/05/20

Cite this

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title = "Convergence to Periodic Regimes in Nonlinear Feedback Systems with a Strongly Convex Backlash",

abstract = "This paper considers a class of nonlinear systems consisting of a linear part with an external input and a nonlinear feedback with a backlash. Assuming that the latter is specified by a strongly convex set, we establish estimates for the Lyapunov exponents which quantify the rate of convergence of the system trajectories to a forced periodic regime when the input is a periodic function of time. These results employ enhanced dissipation inequalities for differential inclusions with strongly convex sets, which were used previously for the Moreau sweeping process.",

author = "Vladimirov, {Igor G.} and Petersen, {Ian R.}",

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year = "2020",

month = may,

language = "English",

series = "European Control Conference 2020, ECC 2020",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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Vladimirov, IG & Petersen, IR 2020, Convergence to Periodic Regimes in Nonlinear Feedback Systems with a Strongly Convex Backlash. in European Control Conference 2020, ECC 2020., 9143648, European Control Conference 2020, ECC 2020, Institute of Electrical and Electronics Engineers Inc., pp. 71-76, 18th European Control Conference, ECC 2020, Saint Petersburg, Russian Federation, 12/05/20.

Convergence to Periodic Regimes in Nonlinear Feedback Systems with a Strongly Convex Backlash. / Vladimirov, Igor G.; Petersen, Ian R.
European Control Conference 2020, ECC 2020. Institute of Electrical and Electronics Engineers Inc., 2020. p. 71-76 9143648 (European Control Conference 2020, ECC 2020).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - This paper considers a class of nonlinear systems consisting of a linear part with an external input and a nonlinear feedback with a backlash. Assuming that the latter is specified by a strongly convex set, we establish estimates for the Lyapunov exponents which quantify the rate of convergence of the system trajectories to a forced periodic regime when the input is a periodic function of time. These results employ enhanced dissipation inequalities for differential inclusions with strongly convex sets, which were used previously for the Moreau sweeping process.

AB - This paper considers a class of nonlinear systems consisting of a linear part with an external input and a nonlinear feedback with a backlash. Assuming that the latter is specified by a strongly convex set, we establish estimates for the Lyapunov exponents which quantify the rate of convergence of the system trajectories to a forced periodic regime when the input is a periodic function of time. These results employ enhanced dissipation inequalities for differential inclusions with strongly convex sets, which were used previously for the Moreau sweeping process.

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M3 - Conference contribution

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BT - European Control Conference 2020, ECC 2020

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 18th European Control Conference, ECC 2020

Y2 - 12 May 2020 through 15 May 2020

ER -

Convergence to Periodic Regimes in Nonlinear Feedback Systems with a Strongly Convex Backlash

Abstract

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