Question

2. Consider the nonlinear model: $\dot{x}_1 = \sin(x_1) + x_2$ $\dot{x}_2 = x_1x_2 + u$ (a) Show that for any $z$, there is an equilibrium $(x_0, u_0)$ where the first component of $x_0$ is $z$, i.e., $x_0 = \begin{pmatrix} z \ * \end{pmatrix}$

          2. Consider the nonlinear model:
$\dot{x}_1 = \sin(x_1) + x_2$
$\dot{x}_2 = x_1x_2 + u$
(a) Show that for any $z$, there is an equilibrium $(x_0, u_0)$ where the first component of $x_0$ is $z$, i.e.,
$x_0 = \begin{pmatrix} z \ * \end{pmatrix}$

2. Consider the nonlinear model:
ẋ1 = sin(x1) + x2
ẋ2 = x1x2 + u
(a) Show that for any z, there is an equilibrium (x0, u0) where the first component of x0 is z, i.e.,
x0 =
< p m a t r i x >

Added by Michelle O.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Consider the nonlinear model: dx1/dt = sin(x1) + x2 dx2/dt = x1*x2 + u (a) Show that for any z, there is an equilibrium (xo, uo) where the first component of xo is z, i.e., xo = [z, **] 2. Consider the nonlinear model: 1 = sin(x + x2) 2 = 12 + (a) Show that for any z, there is an equilibrium (ou) where the first component of is z, i.e.,