diff --git a/control/statesp.py b/control/statesp.py
index 1f5e09ccd..80da2a5f8 100644
--- a/control/statesp.py
+++ b/control/statesp.py
@@ -55,7 +55,7 @@
dot, empty, exp, eye, matrix, ones, pi, poly, poly1d, roots, shape, sin, \
zeros, squeeze
from numpy.random import rand, randn
-from numpy.linalg import inv, det, solve
+from numpy.linalg import solve, eigvals, matrix_rank
from numpy.linalg.linalg import LinAlgError
from scipy.signal import lti, cont2discrete
# from exceptions import Exception
@@ -405,7 +405,7 @@ def freqresp(self, omega):
def pole(self):
"""Compute the poles of a state space system."""
- return roots(poly(self.A))
+ return eigvals(self.A)
def zero(self):
"""Compute the zeros of a state space system."""
@@ -452,21 +452,24 @@ def feedback(self, other=1, sign=-1):
D2 = other.D
F = eye(self.inputs) - sign * D2 * D1
- if abs(det(F)) < 1.e-6:
+ if matrix_rank(F) != self.inputs:
raise ValueError("I - sign * D2 * D1 is singular.")
- E = inv(F)
- T1 = eye(self.outputs) + sign * D1 * E * D2
- T2 = eye(self.inputs) + sign * E * D2 * D1
+ # Precompute F\D2 and F\C2 (E = inv(F))
+ E_D2 = solve(F, D2)
+ E_C2 = solve(F, C2)
+
+ T1 = eye(self.outputs) + sign * D1 * E_D2
+ T2 = eye(self.inputs) + sign * E_D2 * D1
A = concatenate(
(concatenate(
- (A1 + sign * B1 * E * D2 * C1, sign * B1 * E * C2), axis=1),
+ (A1 + sign * B1 * E_D2 * C1, sign * B1 * E_C2), axis=1),
concatenate(
- (B2 * T1 * C1, A2 + sign * B2 * D1 * E * C2), axis=1)),
+ (B2 * T1 * C1, A2 + sign * B2 * D1 * E_C2), axis=1)),
axis=0)
B = concatenate((B1 * T2, B2 * D1 * T2), axis=0)
- C = concatenate((T1 * C1, sign * D1 * E * C2), axis=1)
+ C = concatenate((T1 * C1, sign * D1 * E_C2), axis=1)
D = D1 * T2
return StateSpace(A, B, C, D, dt)
diff --git a/control/tests/statesp_test.py b/control/tests/statesp_test.py
index 0c969b1e1..c19f4f38b 100644
--- a/control/tests/statesp_test.py
+++ b/control/tests/statesp_test.py
@@ -32,12 +32,13 @@ def setUp(self):
def testPole(self):
"""Evaluate the poles of a MIMO system."""
- p = self.sys1.pole()
-
- np.testing.assert_array_almost_equal(p, [3.34747678408874,
+ p = np.sort(self.sys1.pole())
+ true_p = np.sort([3.34747678408874,
-3.17373839204437 + 1.47492908003839j,
-3.17373839204437 - 1.47492908003839j])
+ np.testing.assert_array_almost_equal(p, true_p)
+
def testZero(self):
"""Evaluate the zeros of a SISO system."""
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