Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Equivalence of Linear Complementarity Problems: Theory and Application to Nonsmooth Bifurcations

Abstract : Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear complementarity systems. Mimicking the program that led to the foundation of bifurcation theory in smooth maps, we introduce a novel notion of equivalence between linear complementarity problems that sets the basis for a theory of bifurcations in a large class of nonsmooth maps, including, but not restricted to, steadystate bifurcations in linear complementarity systems. Our definition exploits the rich geometry of linear complementarity problems and leads to constructive algebraic conditions for identifying and classifying the nonsmooth singularities associated with nonsmooth bifurcations. We thoroughly illustrate our theory on an extended applied example, the design of bistability in an electrical network, and a more theoretical one, the identification and classification of all possible equivalence classes in two-dimensional linear complementarity problems.
Complete list of metadata

https://hal.inria.fr/hal-03319638
Contributor : Felix MIranda-Villatoro Connect in order to contact the contributor
Submitted on : Friday, August 13, 2021 - 5:33:15 PM
Last modification on : Monday, August 8, 2022 - 5:38:05 PM
Long-term archiving on: : Sunday, November 14, 2021 - 6:02:42 PM

Files

main.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03319638, version 1
  • ARXIV : 2108.06917

Collections

Citation

Felix Miranda-Villatoro, Fernando Castaños, Alessio Franci. Equivalence of Linear Complementarity Problems: Theory and Application to Nonsmooth Bifurcations. 2021. ⟨hal-03319638⟩

Share

Metrics

Record views

39

Files downloads

108