Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  define the notion of bisimulation relations for DAE systems having a regular matrix pencil. It is ll-known that under the assumption of regularity of the matrix pencil the state vector of the DAE system can be split into two parts: one corresponding to the “ordinary” input-state-output behavior corresponding to a standard proper transfer matrix, and the other one related to a polynomial transfer matrix. Employing the corresponding Wong sequences,  develop the notion of bisimulation relation beten two regular matrix pencil DAE systems, being the direct product of two partial bisimulation relations corresponding to the fast and the slow subsystems.
['Noorma Yulia Megawati', 'Arjan van der Schaft']
I am writing a research paper on a idea Equivalence of regular matrix pencil DAE systems by bisimulation
[{"from": "human", "value": "I am writing a research paper on a idea Equivalence of regular matrix pencil DAE systems by bisimulation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  define the notion of bisimulation relations for DAE systems having a regular matrix pencil. It is ll-known that under the assumption of regularity of the matrix pencil the state vector of the DAE system can be split into two parts: one corresponding to the \u201cordinary\u201d input-state-output behavior corresponding to a standard proper transfer matrix, and the other one related to a polynomial transfer matrix. Employing the corresponding Wong sequences,  develop the notion of bisimulation relation beten two regular matrix pencil DAE systems, being the direct product of two partial bisimulation relations corresponding to the fast and the slow subsystems."}]