A generic ellipsoid abstract domain for linear time invariant systems

Pierre Roux, Romain Jobredeaux, Pierre Loïc Garoche, Éric Féron

Research output: Chapter in Book/Report/Conference proceedingConference contribution

40 Scopus citations


Embedded system control often relies on linear systems, which admit quadratic invariants. The parts of the code that host linear system implementations need dedicated analysis tools, since intervals or linear abstract domains will give imprecise results, if any at all, on these systems. Previous work by FERET proposes a specific abstraction for digital filters that addresses this issue on a specific class of controllers. This paper aims at generalizing the idea. It works directly on system representation, relying on existing methods from control theory to automatically generate quadratic invariants for linear time invariant systems, whose stability is provable. This class encompasses n-th order digital filters and, in general, controllers embedded in critical systems. While control theorists only focus on the existence of such invariants, this paper proposes a method to effectively compute tight ones. The method has been implemented and applied to some benchmark systems, giving good results. It also considers floating points issues and validates the soundness of the computed invariants. Copyright 2012 ACM..
Original languageEnglish (US)
Title of host publicationHSCC'12 - Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control
Number of pages10
StatePublished - May 10 2012
Externally publishedYes

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