Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.   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.  show that this kernel is a non-convex polygon and  give a non-iterative algorithm for computing the coordinates of its vertexes and edges. Moreover,  show some properties of such systems' simple cycles.
['Gerardo Schneider']
I am writing a research paper on a idea Computing invariance kernels of polygonal hybrid systems
[{"from": "human", "value": "I am writing a research paper on a idea Computing invariance kernels of polygonal hybrid systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.   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.  show that this kernel is a non-convex polygon and  give a non-iterative algorithm for computing the coordinates of its vertexes and edges. Moreover,  show some properties of such systems' simple cycles."}]