English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In a previous work we developed a convex infinite dimensional linearprogramming (LP) approach to approximating the region of attraction (ROA) ofpolynomial dynamical systems subject to compact basic semialgebraic stateconstraints. Finite dimensional relaxations to the infinite-dimensional LP leadto a truncated moment problem in the primal and a polynomial sum-of-squaresproblem in the dual. This primal-dual linear matrix inequality (LMI) problemcan be solved numerically with standard semidefinite programming solvers,producing a hierarchy of outer (i.e. exterior) approximations of the ROA bypolynomial sublevel sets, with a guarantee of almost uniform and set-wiseconvergence. In this companion paper, we show that our approach is flexibleenough to be modified so as to generate a hierarchy of polynomial inner(i.e.\,interior) approximations of the ROA with similar convergence guarantees.

Inner approximations of the region of attraction for polynomial dynamical systems