Chapter 6.P2, Problem 9P

For the three-mass system, find a scalar control $u\left(t\right)$ that, when applied to the first mass, will drive the system(16) from the initial state $y\left(0\right)={\left[-1,1,2,0,0,0\right]}^T$ to equilibrium at time $T=10$. Plot the graphs of $u\left(t\right)$ and $y_j\left(t\right),j=1,\dots ,6$ to confirm that the system is actually driven toequilibrium.

$\frac{dy}{dt}=\text{A}y+\text{Bu}(t),$ (16)