Find the invertible matrix \(V\) for which the coordinate transformation
\(x = Vz\)
would establish an equivalence between the two systems
\(\dot{x} = Ax + Bu\)
and
\(\dot{z} = Fz + Gu.\)
All problem data are given as follows:
Matlab/Octave
Mathematica
Python
R
SymPy
import numpy as np
A = np.array([[0.1, -1.0, 0.7], [-0.8, 0.1, -0.5], [-0.9, -0.7, -0.3]])
B = np.array([[0.6], [0.4], [1.0]])
F = np.array([[-4.1, -0.2, -1.1], [5.0, 1.8, 0.7], [11.6, 2.7, 2.2]])
G = np.array([[-2.6], [3.2], [7.4]])
copy this text
V =
matrix (rtol=0.01, atol=1e-08)
