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Model Checking Polygonal Differential Inclusions Using Invariance Kernels
 In VMCAI’04, number 2937 in LNCS
, 2004
"... Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. Here, we identify and compute an important object of such systems' phase portrait, namely invariance kernels. An invariant set is a set of initial points of ..."
Abstract

Cited by 9 (9 self)
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Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. Here, we identify and compute an important object of such systems' phase portrait, namely invariance kernels. An invariant set is a set of initial points of trajectories which keep rotating in a cycle forever and the invariance kernel is the largest of such sets. We show that this kernel is a nonconvex polygon and we give a noniterative algorithm for computing the coordinates of its vertices and edges. Moreover, we present a breadthfirst search algorithm for solving the reachability problem for such systems. Invariance kernels play an important role in the algorithm.
Computing Invariance Kernels of Polygonal Hybrid Systems
 NORDIC JOURNAL OF COMPUTING
, 2004
"... 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 behav ..."
Abstract

Cited by 7 (5 self)
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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 nonconvex polygon and we give a noniterative algorithm for computing the coordinates of its vertexes and edges. Moreover, we show some properties of such systems’ simple cycles.