Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on the space of continuous functions.  give an explicit parameterization of a sequence of finite-dimensional subsets of the cone of positive Lyapunov functions using positive semidefinite matrices. This allows stability analysis of linear time-delay systems to be formulated as a semidefinite program.
['Matthew M. Peet', 'Antonis Papachristodoulou', 'Sanjay Lall']
I am writing a research paper on a idea Positive Forms and Stability of Linear Time-Delay Systems
[{"from": "human", "value": "I am writing a research paper on a idea Positive Forms and Stability of Linear Time-Delay Systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on the space of continuous functions.  give an explicit parameterization of a sequence of finite-dimensional subsets of the cone of positive Lyapunov functions using positive semidefinite matrices. This allows stability analysis of linear time-delay systems to be formulated as a semidefinite program."}]