Find a control function u(t) : [0, infinity) -> R such that (1) l u(t) l smaller than or equal to 2 for all t in [0, infinity) and (2) u steers \begin{pmatrix}1\\ 1\end{pmatrix} to \begin{pmatrix}0\\ 0\end{pmatrix} where the control system is given by \begin{pmatrix}x\\ y\end{pmatrix}^'=\begin{pmatrix}0&1\\ -1&0\end{pmatrix}\begin{pmatrix}x\\ y\end{pmatrix}+\begin{pmatrix}0\\ 1\end{pmatrix}u\left(t\right). Use Analysis to solve the problem.

Find a control function u(t) : [0, infinity) -> R such that (1) l u(t) l smaller than or equal to 2 for all t in [0, infinity) and (2) u steers \begin{pmatrix}1\\ 1\end{pmatrix} to \begin{pmatrix}0\\ 0\end{pmatrix} where the control system is given by \begin{pmatrix}x\\ y\end{pmatrix}^'=\begin{pmatrix}0&1\\ -1&0\end{pmatrix}\begin{pmatrix}x\\ y\end{pmatrix}+\begin{pmatrix}0\\ 1\end{pmatrix}u\left(t\right). Use Analysis to solve the problem.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 30E

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