I have to find the equilibrium points of a nonlinear system:
x1' = .51*sqrt(x1) + .076*u
x2' = -.51*sqrt(x1) + .51*sqrt(x2) + .136*u
I have assumed that u is arbitrary, so I substituted it for 1. So far I have equated
x1' = .51*sqrt(x1bar) + .076 = 0
x2' = -.51*sqrt(x1bar) + .51*sqrt(x2bar) + .136 = 0
which resulted in
sqrt(x1bar) = -.076/.51
x1bar = .0222
-.51(sqrt(x1bar) - sqrt(x2bar)) = -.136
sqrt(.0222) - sqrt(x2bar) = .136/.51
x2bar = .01384
xbar = (.0222, .01384)
Then I took the Jacobian of the system for the points above
J(x,y) = [1.71 0 ]
[ -1.71 2.1675]
Am I on the right track or have I done this completely wrong?