Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a method for complexity reduction in reachability analysis and controller synthesis via a Schur-based decomposition for LTI systems. The decomposition yields either decoupled or akly-coupled subsystems, each of lor dimension than the original system. Reachable sets, computed for each subsystem, are back-projected and intersected to yield an overapproximation of the actual reachable set. Evaluating our method for a variety of examples (3D, 4D, and 8D),  show that significant reduction in the computational costs can be achieved. This technique has considerable potential utility for use in conjunction with computationally intensive reachability tools.
['Shahab Kaynama', 'Meeko M. K. Oishi']
I am writing a research paper on a idea Schur-based decomposition for reachability analysis of linear time-invariant systems
[{"from": "human", "value": "I am writing a research paper on a idea Schur-based decomposition for reachability analysis of linear time-invariant systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a method for complexity reduction in reachability analysis and controller synthesis via a Schur-based decomposition for LTI systems. The decomposition yields either decoupled or akly-coupled subsystems, each of lor dimension than the original system. Reachable sets, computed for each subsystem, are back-projected and intersected to yield an overapproximation of the actual reachable set. Evaluating our method for a variety of examples (3D, 4D, and 8D),  show that significant reduction in the computational costs can be achieved. This technique has considerable potential utility for use in conjunction with computationally intensive reachability tools."}]