Question

1. A state space linear system is shown below.

dx1(t)/dt=x1(t)+x2(t)-x3(t)+u1(t)

dx2(t)/dt=--x3(t)-u1(t)

dx3(t)/dt=-x3(t)-u2(t)

y(t)=-x1(t)+x3(t)

(1) Re-write the state space equation as following, determine matrices A, B, C and D

dx(t)/at=Ax+Bu

y(t)=Cx+Du

(2) Determine the matrix Q that is

Q=[B A*B (A^2)*B (A^3)*B L (A^(n-1)*B]

(3) Determine if the rank of Q is n (n=3) and determine if the system is controllable

Answer 1