873 research outputs found
Input-to-state stability of unbounded bilinear control systems
We study input-to-state stability of bilinear control systems with possibly
unbounded control operators. Natural sufficient conditions for integral
input-to-state stability are given. The obtained results are applied to a
bilinearly controlled Fokker-Planck equation.Comment: 20 pages, completely new version based on the few preliminary ideas
in v1. Compared to v1, the results have been significantly generalized and
extende
Asymptotic ensemble stabilizability of the Bloch equation
In this paper we are concerned with the stabilizability to an equilibrium
point of an ensemble of non interacting half-spins. We assume that the spins
are immersed in a static magnetic field, with dispersion in the Larmor
frequency, and are controlled by a time varying transverse field. Our goal is
to steer the whole ensemble to the uniform "down" position. Two cases are
addressed: for a finite ensemble of spins, we provide a control function (in
feedback form) that asymptotically stabilizes the ensemble in the "down"
position, generically with respect to the initial condition. For an ensemble
containing a countable number of spins, we construct a sequence of control
functions such that the sequence of the corresponding solutions pointwise
converges, asymptotically in time, to the target state, generically with
respect to the initial conditions. The control functions proposed are uniformly
bounded and continuous
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