Find a control function u(t) : [0, infinity) -> R such that (1) l u(t) l smaller than or equal to 2 fr 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).

Find a control function u(t) : [0, infinity) -> R such that (1) l u(t) l smaller than or equal to 2 fr 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).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Find the critical point of ƒ(x, y) = xy + 2x - ln x2y in the open first quadrant (x >0, y>0) and show that ƒ takes on a minimum there.
Integrate f(x, y, z) = x2 -y + z over the line segments from (0, 0, 0) to (1, 1, 0) and then to the point (1, 1, 1).
What can you conclude about a real function f(x,y) that has continuous partial derivatives at a point (x,y)?
Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 1, 0) and then to the point (1,1, 1).
A function f has continuous second partial derivatives on an open region containing the critical point (a, b). If fxx(a, b) and fyy(a, b) have opposite signs, what is implied? Explain.
From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)
The function f(x,y) = R x y cos(t2)dt has exactly one critical point in the domain 0 < x < 2, 0 < y < 2. Find this critical point and determine whether it gives a relative maximum, minimum or saddle point for this funciton.
A) Integrate f(x, y) = xy^2 over the square bounded with endpoints at (0, 0), (0, 1), (1, 0) and (1, 1) b) Integrate f(x, y) = x over the triangle whose endpoints are at (0, 0), (1, 0)and (1, 1)