Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A given nonlinear system can be represented via an immersion as rational or polynomial functions, thus leading to a simplified model structure. An immersion is a mapping of the initial state from the original state space to another state space, while exactly preserving the input-output map. In this note  show that the linearization of the system after immersion has an identical input-output map to the linearization of the original system before immersion. In other words, immersion and linearization commute. This is potentially useful for applications such as linear control design and sensitivity analysis after nonlinear identification, and has important implications for system approximation by linearization.
['Toshiyuki Ohtsuka', 'Stefan Streif']
I am writing a research paper on a idea Commutativity of immersion and linearization
[{"from": "human", "value": "I am writing a research paper on a idea Commutativity of immersion and linearization"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A given nonlinear system can be represented via an immersion as rational or polynomial functions, thus leading to a simplified model structure. An immersion is a mapping of the initial state from the original state space to another state space, while exactly preserving the input-output map. In this note  show that the linearization of the system after immersion has an identical input-output map to the linearization of the original system before immersion. In other words, immersion and linearization commute. This is potentially useful for applications such as linear control design and sensitivity analysis after nonlinear identification, and has important implications for system approximation by linearization."}]