### Abstract

Language | English |
---|---|

Number of pages | 13 |

Journal | Control Systems Letters (L-CSS) |

Volume | 2 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jul 2018 |

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**Operator-theoretic characterization of eventually monotone systems.** / Sootla, Aivar; Mauroy, Alexandre.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Operator-theoretic characterization of eventually monotone systems

AU - Sootla, Aivar

AU - Mauroy, Alexandre

PY - 2018/7

Y1 - 2018/7

N2 - Monotone systems are dynamical systems whose solutions preserve a partial order in the initial condition for all positive times. It stands to reason that some systems may preserve a partial order only after some initial transient. These systems are usually called eventually monotone. While monotone systems have a characterization in terms of their vector fields (i.e. Kamke-M¨ uller condition), eventually monotone systems have not been characterized in such an explicit manner. In order to provide a characterization, we drew inspiration from the results for linear systems, where eventually monotone (positive) systems are studied using the spectral properties of the system (i.e. Perron-Frobenius property). In the case of nonlinear systems, this spectral characterization is not straightforward, a fact that explains why the class of eventually monotone systems has received little attention to date. In this paper, we show that a spectral characterization of nonlinear eventually monotone systems can be obtained through the Koopman operator framework. We consider a number of biologically inspired examples to illustrate the potential applicability of eventual monotonicity.

AB - Monotone systems are dynamical systems whose solutions preserve a partial order in the initial condition for all positive times. It stands to reason that some systems may preserve a partial order only after some initial transient. These systems are usually called eventually monotone. While monotone systems have a characterization in terms of their vector fields (i.e. Kamke-M¨ uller condition), eventually monotone systems have not been characterized in such an explicit manner. In order to provide a characterization, we drew inspiration from the results for linear systems, where eventually monotone (positive) systems are studied using the spectral properties of the system (i.e. Perron-Frobenius property). In the case of nonlinear systems, this spectral characterization is not straightforward, a fact that explains why the class of eventually monotone systems has received little attention to date. In this paper, we show that a spectral characterization of nonlinear eventually monotone systems can be obtained through the Koopman operator framework. We consider a number of biologically inspired examples to illustrate the potential applicability of eventual monotonicity.

U2 - 10.1109/LCSYS.2018.2841654

DO - 10.1109/LCSYS.2018.2841654

M3 - Article

VL - 2

JO - Control Systems Letters (L-CSS)

T2 - Control Systems Letters (L-CSS)

JF - Control Systems Letters (L-CSS)

SN - 2475-1456

IS - 3

ER -