Viability theory
Theoretical Computer Science
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
What's decidable about hybrid automata?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Deciding reachability for planar multi-polynomial systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Qualitative Theory of Hybrid Dynamical Systems
Qualitative Theory of Hybrid Dynamical Systems
Widening the Boundary between Decidable and Undecidable Hybrid Systems
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
Viable Control of Hybrid Systems
Hybrid Systems II
Reachability Analysis via Face Lifting
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Towards Computing Phase Portraits of Polygonal Differential Inclusions
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Hybrid Kernels and Capture Basins for Impulse Constrained Systems
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
SPeeDI - A Verification Tool for Polygonal Hybrid Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Reachability Analysis of Planar Multi-limear Systems
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Algorithmic analysis of polygonal hybrid systems, part I: Reachability
Theoretical Computer Science
Algorithmic analysis of polygonal hybrid systems, Part II: Phase portrait and tools
Theoretical Computer Science
Analysing formal models of genetic regulatory networks with delays
International Journal of Bioinformatics Research and Applications
Computation and visualisation of phase portraits for model checking SPDIs
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Static analysis for state-space reduction of polygonal hybrid systems
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
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Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. One way of analysing such systems (and hybrid systems in general) is through the study of their phase portrait, which characterise the systems' qualitative behaviour. In this paper we identify and compute an important object of polygonal hybrid systems' phase portrait, namely invariance kernels. An invariant set is a set of points such That any trajectory starting in such point keep necessarily rotating in the set forever and the invariance, kernel is the largest of such sets. We show that this kernel is a non-convex polygon and we give a non-iterative algorithm for computing the coordinates of its vertexes and edges. Moreover, we show some properties of such systems' simple cycles.