Converse Barrier Certificate Theorems

Rafael Wisniewski, Christoffer Sloth

Research output: Contribution to journalJournal articleResearchpeer-review

36 Citations (Scopus)


This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither singular points nor closed orbits. In this paper, we redefine the standard notion of safety to comply with dynamical systems with multiple singular elements. Hereafter, we prove the converse barrier certificate theorems and highlight the differences between our results and previous work by a number of illustrative examples.
Original languageEnglish
JournalI E E E Transactions on Automatic Control
Issue number5
Pages (from-to)1356-1361
Publication statusPublished - May 2016


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