Question

Find the state equations for the following differential equation: dy(t) dy(t) + 6y(t) = z(t) dt3 dt2 dt +60360) + 11. 1 1 + oz(t) 0 0 -6 -11 X3 X 1 y(t) = [1 0 0] x2 + [0]z(t) X3 X1 0 1 0 = 0 0 0 X2 0 Iz(t) X2 6 11 6 X3 X3 X1 y(t) = [1 1 0] x2 + [O] z (t) X3

Answer 1

Option first is correct for the given differential equation as

For the 3x3 matrix A:

  

the characteristic polynomial can be found using the formula

λ^3- tr(A) λ^2+(A11+A22+A33)λ-det(A)=0

where tr(A) is the trace of A and det(A) is the determinant of A.

Given equation on LHS is just like characteristics polynomial of 3×3 matrix.

So option A is correct