Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Feedback stabilization of an ensemble of non interacting half spins described by the Bloch equations is considered. This system may be seen as an interesting example for infinite dimensional systems with continuous spectra.  propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibrium in the H^1 topology. This local convergence is shown to be a ak asymptotic convergence for the H^1 topology and thus a strong convergence for the C^0 topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the equilibrium.
['Karine Beauchard', 'Paulo Sérgio Pereira da Silva', 'Pierre Rouchon']
I am writing a research paper on a idea Stabilization for an ensemble of half-spin systems
[{"from": "human", "value": "I am writing a research paper on a idea Stabilization for an ensemble of half-spin systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Feedback stabilization of an ensemble of non interacting half spins described by the Bloch equations is considered. This system may be seen as an interesting example for infinite dimensional systems with continuous spectra.  propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibrium in the H^1 topology. This local convergence is shown to be a ak asymptotic convergence for the H^1 topology and thus a strong convergence for the C^0 topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the equilibrium."}]