A necessary and sufficient condition for the controllability of linear systems in Hilbert spaces and applications
نویسندگان
چکیده
As we have announced in the title of this work, we show that a broad class of linear evolution equations are exactly controllable. This class is represented by the following infinite dimensional linear control system: ż = Az + Bu(t), t > 0, z ∈ Z, u(t) ∈ U where Z, U are Hilbert spaces, the control function u belong to L2(0, t1; U), t1 > 0, B ∈ L(U,Z), A generates a strongly continuous semigroup operator T (t) according to [5]. We give necessary and sufficient condition for the exact controllability of this system and apply this results to a linear controlled damped wave equation.
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عنوان ژورنال:
- IMA J. Math. Control & Information
دوره 25 شماره
صفحات -
تاریخ انتشار 2008