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Cari amici,<br>
<br>
vi segnalo il prossimo seminario di ED a Tor Vergata:<br>
<br>
<h2>Martedi' 4 Giugno 2013, h 14:30, Aula Dal Passo
</h2>
<h2>Enrico Priola - Università di Torino
</h2>
<h2>"Linear Operator Inequality and Null Controllability with
Vanishing Energy for unbounded control systems."<br>
<br>
We consider linear systems on a separable Hilbert space $H$, which
are null controllable at some time $T_0>0$ under the action of
a point or boundary control. Parabolic and hyperbolic control
systems usually studied in applications are special cases. To
every initial state $ y_0 \in H$ we associate the minimal "energy"
needed to transfer $ y_0 $ to $ 0 $ in a time $ T \ge T_0$
("energy" of a control being the square of its $ L^2 $ norm). We
give both necessary and sufficient conditions under which the
minimal energy converges to $ 0 $ for $ T\to+\infty $. This
extends to boundary control systems the concept of null
controllability with vanishing energy introduced by Priola and
Zabczyk (Siam J. Control Optim. 42 (2003)) for distributed
systems. The proofs in Priola-Zabczyk paper depend on properties
of the associated Riccati equation, which are not available in the
present, general setting. Here we base our results on new
properties of the quadratic regulator problem with stability and
the Linear Operator Inequality.</h2>
<br>
<pre class="moz-signature" cols="72">--
Daniele Castorina
Dipartimento di Matematica - Studio 1221
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica 00133 Roma
email: <a class="moz-txt-link-abbreviated" href="mailto:castorin@mat.uniroma2.it">castorin@mat.uniroma2.it</a>
tel: +390672594653</pre>
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