def is_min_realisation(A, B, C):
"""
Parameters: A => state space matrix
B => ''
C => ''
Returns: is_min_real => True if the system is the minimum realisation
"""
state_obsr, out_pole_vec, observe_matrix = state_observability(A, C)
state_control, in_pole_vec, control_matrix = state_controllability(A, B)
return state_control and state_obsr
def is_min_realisation(A, B, C):
"""
Parameters: A => state space matrix
B => ''
C => ''
Returns: is_min_real => True if the system is the minimum realisation
"""
state_obsr, out_pole_vec, observe_matrix = state_observability(A, C)
state_control, in_pole_vec, control_matrix = state_controllability(A, B)
return state_control and state_obsr
import scipy.signal as sign from utils import state_controllability, zeros # This module executes Example 4.4. # The controllability Gramian has been included # Define state space matrices A = np.matrix([[-2, -2], [0, -4]]) B = np.matrix([[1], [1]]) C = np.matrix([[1, 0]]) D = np.matrix([[0]]) # Create frequency domain mode; G = sign.lti(A, B, C, D) control, in_vecs, c_matrix = state_controllability(A, B) # Question: Why does A.transpose give the same eigenvectors as the book # and not plain A?? # Answer: The eig function in the numpy library only calculates # the right hand eigenvectors. The Scipy library provides a eig function # in which you can specify whether you want left or right handed eigenvectors. # To determine controllability you need to calculate the input pole vectors # which is dependant on the left eigenvectors. # Calculate eigen vectors and pole vectors val, vec = LA.eig(A, None, 1, 0, 0, 0) n = lin.matrix_rank(c_matrix) P = LA.solve_continuous_lyapunov(A, -B * B.T)
from utils import state_controllability, zeros
# This module executes Example 4.4.
# The controllability Gramian has been included
# Define state space matrices
A = np.matrix([[-2, -2],
[0, -4]])
B = np.matrix([[1],
[1]])
C = np.matrix([[1, 0]])
D = np.matrix([[0]])
# Create frequency domain mode;
G = sign.lti(A, B, C, D)
control, in_vecs, c_matrix = state_controllability(A, B)
# Question: Why does A.transpose give the same eigenvectors as the book
# and not plain A??
# Answer: The eig function in the numpy library only calculates
# the right hand eigenvectors. The Scipy library provides a eig function
# in which you can specify whether you want left or right handed eigenvectors.
# To determine controllability you need to calculate the input pole vectors
# which is dependant on the left eigenvectors.
# Calculate eigen vectors and pole vectors
val, vec = LA.eig(A, None, 1, 0, 0, 0)
n = lin.matrix_rank(c_matrix)
P = LA.solve_lyapunov(A, -B * B.T)