Stability of Non-Negative Lur'e Systems

Adam Bill; Christopher Guiver; Hartmut Logemann; Stuart Townley

doi:10.1137/140994599

Stability of Non-Negative Lur'e Systems

Adam Bill, Christopher Guiver, Hartmut Logemann, Stuart Townley

University of Exeter

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Abstract

A stability/instability trichotomy for a class of nonnegative continuous-time Lur’e systems is derived. Asymptotic, exponential, and input-to-state stability concepts are considered. The presented trichotomy rests on Perron–Frobenius theory, absolute stability theory, and recent input-to-state stability results for Lur’e systems. Applications of the results derived arise in various fields, including density-dependent population dynamics, and two examples are discussed in detail.

Original language	English
Pages (from-to)	1176-1211
Number of pages	36
Journal	SIAM Journal on Control and Optimization
Volume	54
Issue number	3
DOIs	https://doi.org/10.1137/140994599
Publication status	Published - 12 May 2016

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10.1137/140994599Licence: CC BY

Hartmut Logemann
- Department of Mathematical Sciences - Professor Emeritus
Person: Honorary / Visiting Staff

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title = "Stability of Non-Negative Lur'e Systems",

abstract = "A stability/instability trichotomy for a class of nonnegative continuous-time Lur{\textquoteright}e systems is derived. Asymptotic, exponential, and input-to-state stability concepts are considered. The presented trichotomy rests on Perron–Frobenius theory, absolute stability theory, and recent input-to-state stability results for Lur{\textquoteright}e systems. Applications of the results derived arise in various fields, including density-dependent population dynamics, and two examples are discussed in detail.",

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T1 - Stability of Non-Negative Lur'e Systems

AU - Bill, Adam

AU - Guiver, Christopher

AU - Logemann, Hartmut

AU - Townley, Stuart

PY - 2016/5/12

Y1 - 2016/5/12

N2 - A stability/instability trichotomy for a class of nonnegative continuous-time Lur’e systems is derived. Asymptotic, exponential, and input-to-state stability concepts are considered. The presented trichotomy rests on Perron–Frobenius theory, absolute stability theory, and recent input-to-state stability results for Lur’e systems. Applications of the results derived arise in various fields, including density-dependent population dynamics, and two examples are discussed in detail.

AB - A stability/instability trichotomy for a class of nonnegative continuous-time Lur’e systems is derived. Asymptotic, exponential, and input-to-state stability concepts are considered. The presented trichotomy rests on Perron–Frobenius theory, absolute stability theory, and recent input-to-state stability results for Lur’e systems. Applications of the results derived arise in various fields, including density-dependent population dynamics, and two examples are discussed in detail.

U2 - 10.1137/140994599

DO - 10.1137/140994599

M3 - Article

VL - 54

SP - 1176

EP - 1211

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 3

ER -

Stability of Non-Negative Lur'e Systems

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Hartmut Logemann

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