diff --git a/control/statefbk.py b/control/statefbk.py
index a29e86ef7..3d2ef6d9c 100644
--- a/control/statefbk.py
+++ b/control/statefbk.py
@@ -990,13 +990,15 @@ def _control_output(t, states, inputs, params):
return ctrl, closed
-def ctrb(A, B):
+def ctrb(A, B, t=None):
"""Controllabilty matrix.
Parameters
----------
A, B : array_like or string
Dynamics and input matrix of the system
+ t : None or integer
+ maximum time horizon of the controllability matrix, max = A.shape[0]
Returns
-------
@@ -1016,22 +1018,30 @@ def ctrb(A, B):
amat = _ssmatrix(A)
bmat = _ssmatrix(B)
n = np.shape(amat)[0]
+ m = np.shape(bmat)[1]
+
+ if t is None or t > n:
+ t = n
# Construct the controllability matrix
- ctrb = np.hstack(
- [bmat] + [np.linalg.matrix_power(amat, i) @ bmat
- for i in range(1, n)])
+ ctrb = np.zeros((n, t * m))
+ ctrb[:, :m] = bmat
+ for k in range(1, t):
+ ctrb[:, k * m:(k + 1) * m] = np.dot(amat, ctrb[:, (k - 1) * m:k * m])
+
return _ssmatrix(ctrb)
-def obsv(A, C):
+def obsv(A, C, t=None):
"""Observability matrix.
Parameters
----------
A, C : array_like or string
Dynamics and output matrix of the system
-
+ t : None or integer
+ maximum time horizon of the controllability matrix, max = A.shape[0]
+
Returns
-------
O : 2D array (or matrix)
@@ -1050,10 +1060,18 @@ def obsv(A, C):
amat = _ssmatrix(A)
cmat = _ssmatrix(C)
n = np.shape(amat)[0]
+ p = np.shape(cmat)[0]
+
+ if t is None or t > n:
+ t = n
# Construct the observability matrix
- obsv = np.vstack([cmat] + [cmat @ np.linalg.matrix_power(amat, i)
- for i in range(1, n)])
+ obsv = np.zeros((t * p, n))
+ obsv[:p, :] = cmat
+
+ for k in range(1, t):
+ obsv[k * p:(k + 1) * p, :] = np.dot(obsv[(k - 1) * p:k * p, :], amat)
+
return _ssmatrix(obsv)
diff --git a/control/tests/statefbk_test.py b/control/tests/statefbk_test.py
index d605c9be7..cb677b40a 100644
--- a/control/tests/statefbk_test.py
+++ b/control/tests/statefbk_test.py
@@ -49,6 +49,14 @@ def testCtrbMIMO(self):
Wc = ctrb(A, B)
np.testing.assert_array_almost_equal(Wc, Wctrue)
+ def testCtrbT(self):
+ A = np.array([[1., 2.], [3., 4.]])
+ B = np.array([[5., 6.], [7., 8.]])
+ t = 1
+ Wctrue = np.array([[5., 6.], [7., 8.]])
+ Wc = ctrb(A, B, t=t)
+ np.testing.assert_array_almost_equal(Wc, Wctrue)
+
def testObsvSISO(self):
A = np.array([[1., 2.], [3., 4.]])
C = np.array([[5., 7.]])
@@ -62,6 +70,14 @@ def testObsvMIMO(self):
Wotrue = np.array([[5., 6.], [7., 8.], [23., 34.], [31., 46.]])
Wo = obsv(A, C)
np.testing.assert_array_almost_equal(Wo, Wotrue)
+
+ def testObsvT(self):
+ A = np.array([[1., 2.], [3., 4.]])
+ C = np.array([[5., 6.], [7., 8.]])
+ t = 1
+ Wotrue = np.array([[5., 6.], [7., 8.]])
+ Wo = obsv(A, C, t=t)
+ np.testing.assert_array_almost_equal(Wo, Wotrue)
def testCtrbObsvDuality(self):
A = np.array([[1.2, -2.3], [3.4, -4.5]])
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