Cone-Copositive Lyapunov Functions for Complementarity Systems: Converse Result and Polynomial Approximation
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Cone-Copositive Lyapunov Functions for Complementarity Systems: Converse Result and Polynomial Approximation
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
20205 - Automation and control systems
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IEEE Transactions on Automatic Control
ISSN
0018-9286
e-ISSN
1558-2523
Volume of the periodical
67
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
1253-1268
UT code for WoS article
000761219400016
EID of the result in the Scopus database
2-s2.0-85101773828