10,101 research outputs found
On the stabilization of persistently excited linear systems
We consider control systems of the type , where
, is a controllable pair and is an unknown
time-varying signal with values in satisfying a persistent excitation
condition i.e., \int_t^{t+T}\al(s)ds\geq \mu for every , with
independent on . We prove that such a system is stabilizable
with a linear feedback depending only on the pair if the eigenvalues
of have non-positive real part. We also show that stabilizability does not
hold for arbitrary matrices . Moreover, the question of whether the system
can be stabilized or not with an arbitrarily large rate of convergence gives
rise to a bifurcation phenomenon in dependence of the parameter
Bimeron nanoconfined design
We report on the stabilization of the topological bimeron excitations in
confined geometries. The Monte Carlo simulations for a ferromagnet with a
strong Dzyaloshinskii-Moriya interaction revealed the formation of a mixed
skyrmion-bimeron phase. The vacancy grid created in the spin lattice
drastically changes the picture of the topological excitations and allows one
to choose between the formation of a pure bimeron and skyrmion lattice. We
found that the rhombic plaquette provides a natural environment for
stabilization of the bimeron excitations. Such a rhombic geometry can protect
the topological state even in the absence of the magnetic field.Comment: 5 pages, 7 figure
A characterization of switched linear control systems with finite L 2 -gain
Motivated by an open problem posed by J.P. Hespanha, we extend the notion of
Barabanov norm and extremal trajectory to classes of switching signals that are
not closed under concatenation. We use these tools to prove that the finiteness
of the L2-gain is equivalent, for a large set of switched linear control
systems, to the condition that the generalized spectral radius associated with
any minimal realization of the original switched system is smaller than one
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