Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the stability of second-order switched homogeneous systems. Using the concept of generalized first integrals  explicitly characterize the "most destabilizing" switching-law and construct a Lyapunov function that yields an easily verifiable, necessary and sufficient condition for asymptotic stability. Using the duality beten stability analysis and control synthesis, this also leads to a novel algorithm for designing a stabilizing switching controller.
['David Holcman', 'Michael Margaliot']
I am writing a research paper on a idea Stability Analysis of Second-Order Switched Homogeneous Systems
[{"from": "human", "value": "I am writing a research paper on a idea Stability Analysis of Second-Order Switched Homogeneous Systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the stability of second-order switched homogeneous systems. Using the concept of generalized first integrals  explicitly characterize the \"most destabilizing\" switching-law and construct a Lyapunov function that yields an easily verifiable, necessary and sufficient condition for asymptotic stability. Using the duality beten stability analysis and control synthesis, this also leads to a novel algorithm for designing a stabilizing switching controller."}]