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Bounded Control Operators: Control Inside the Domain

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Abstract

As in Chapter 1 (Part IV) we consider a dynamical system governed by the following state equation:
$$ \left\{ \begin{gathered} x'(t) = Ax(t) + Bu(t),{\text{ }}t \geqslant 0, \hfill \\ x(0) = x_0 \in H, \hfill \\ \end{gathered} \right. $$
(1.1)
and we use the notation introduced in §1 of that chapter. We assume that
$$ (\mathcal{H})\infty \left\{ \begin{gathered} (i){\text{ }}A{\text{ generates a }}C_0 {\text{ semigroup }}e^{tA} {\text{ in }}H{\text{,}} \hfill \\ (ii){\text{ }}B \in \mathcal{L}(U;H), \hfill \\ (iii){\text{ }}C \in \mathcal{L}(U;H). \hfill \\ \end{gathered} \right. $$
Clearly, if the assumptions \( (\mathcal{H})_\infty \) hold, then the assumptions \( (\mathcal{H}) \) of §1 in Chapter 1 (Part IV) are verified with P0 = 0.

Keywords

Periodic Solution Riccati Equation Mild Solution Minimal Solution Admissible Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2007

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