Cone-Copositive Lyapunov Functions for Complementarity Systems: Converse Result and Polynomial Approximation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00356559" target="_blank" >RIV/68407700:21230/22:00356559 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1109/TAC.2021.3061557" target="_blank" >https://doi.org/10.1109/TAC.2021.3061557</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/TAC.2021.3061557" target="_blank" >10.1109/TAC.2021.3061557</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cone-Copositive Lyapunov Functions for Complementarity Systems: Converse Result and Polynomial Approximation

Popis výsledku v původním jazyce

This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential equation coupled with a set-valued relation that introduces discontinuities in the vector field at the boundaries of the constraint set. In particular, the set-valued relation is described by the subdifferential of the indicator function of a closed convex cone, which results in a cone-complementarity system. The question of analyzing the stability of such systems is addressed by constructing cone-copositive Lyapunov functions. As a first analytical result, we show that exponentially stable complementarity systems always admit a continuously differentiable cone-copositive Lyapunov function. Putting some more structure on the system vector field, such as homogeneity, we can show that the aforementioned functions can be approximated by a rational function of cone-copositive homogeneous polynomials. This latter class of functions is seen to be particularly amenable for numerical computation as we provide two types of algorithms for precisely that purpose. These algorithms consist of a hierarchy of either linear or semidefinite optimization problems for computing the desired cone-copositive Lyapunov function. Some examples are given to illustrate our approach.

Název v anglickém jazyce

Cone-Copositive Lyapunov Functions for Complementarity Systems: Converse Result and Polynomial Approximation

Popis výsledku anglicky

This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential equation coupled with a set-valued relation that introduces discontinuities in the vector field at the boundaries of the constraint set. In particular, the set-valued relation is described by the subdifferential of the indicator function of a closed convex cone, which results in a cone-complementarity system. The question of analyzing the stability of such systems is addressed by constructing cone-copositive Lyapunov functions. As a first analytical result, we show that exponentially stable complementarity systems always admit a continuously differentiable cone-copositive Lyapunov function. Putting some more structure on the system vector field, such as homogeneity, we can show that the aforementioned functions can be approximated by a rational function of cone-copositive homogeneous polynomials. This latter class of functions is seen to be particularly amenable for numerical computation as we provide two types of algorithms for precisely that purpose. These algorithms consist of a hierarchy of either linear or semidefinite optimization problems for computing the desired cone-copositive Lyapunov function. Some examples are given to illustrate our approach.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

IEEE Transactions on Automatic Control

ISSN

0018-9286

e-ISSN

1558-2523

Svazek periodika

67

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

1253-1268

Kód UT WoS článku

000761219400016

EID výsledku v databázi Scopus

2-s2.0-85101773828