On Attainable Set and Controllability for Abstract Control Problem with Unbounded Input Operator

Details On Attainable Set and Controllability for Abstract Control Problem with Unbounded Input Operator On Attainable Set and Controllability for Abstract Control Problem with Unbounded Input Operator

1998-12-17

arxiv.org/abs/math/9812102v2

Mathematics

Dynamical Systems

19 pages, LaTeX, no figures

Scientific paper

For linear evolution control system described by $\dot{x}=Ax(t)+Bu(t),x(0)=x_{0}$ ($A$ generates a strongly continuous semigroup ${S(t)}_{t\ge 0}$ in a Banach space $X$; $B$ is a linear unbounded operator), the attainable set $K(t)$ is studied. Conditions of the independence of $t$ for its closure $\bar{K(t)}$ are established. Controllability conditions for some classes of evolution systems are obtained.

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