Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider coupled systems consisting of a ll-posed and strictly proper (hence regular) subsystem and a finite-dimensional subsystem connected in feedback. The external world interacts with the coupled system via the finite-dimensional part, which receives the external input and sends out the output. Under several assumptions,  derive ll-posedness, regularity, exact (or approximate) controllability and exact (or approximate) observability results for such coupled systems.
['Xiaowei Zhao', 'George Weiss']
I am writing a research paper on a idea Controllability and Observability of a Well-Posed System Coupled With a Finite-Dimensional System
[{"from": "human", "value": "I am writing a research paper on a idea Controllability and Observability of a Well-Posed System Coupled With a Finite-Dimensional System"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider coupled systems consisting of a ll-posed and strictly proper (hence regular) subsystem and a finite-dimensional subsystem connected in feedback. The external world interacts with the coupled system via the finite-dimensional part, which receives the external input and sends out the output. Under several assumptions,  derive ll-posedness, regularity, exact (or approximate) controllability and exact (or approximate) observability results for such coupled systems."}]