Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract    prove the existence of positive linear switching systems (continuous time), whose trajectories grow to infinity, but slor than a given increasing function. This implies that, unlike the situation with linear ODE, the maximal growth of trajectories of linear systems may be arbitrarily slow. For systems generated by a finite set of matrices, this phenomenon is proved to be impossible in dimension   2  , while in all bigger dimensions the sublinear growth may occur. The corresponding examples are provided and several open problems are formulated.
['Vladimir Protasov']
I am writing a research paper on a idea Linear switching systems with slow growth of trajectories
[{"from": "human", "value": "I am writing a research paper on a idea Linear switching systems with slow growth of trajectories"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract    prove the existence of positive linear switching systems (continuous time), whose trajectories grow to infinity, but slor than a given increasing function. This implies that, unlike the situation with linear ODE, the maximal growth of trajectories of linear systems may be arbitrarily slow. For systems generated by a finite set of matrices, this phenomenon is proved to be impossible in dimension   2  , while in all bigger dimensions the sublinear growth may occur. The corresponding examples are provided and several open problems are formulated."}]