@@ -52,3 +52,51 @@ def test_unreachable_system(self):
5252
5353 # Check if an exception is raised
5454 np .testing .assert_raises (ValueError , canonical_form , sys , "reachable" )
55+
56+ def test_observable_form (self ):
57+ """Test the observable canonical form"""
58+
59+ # Create a system in the observable canonical form
60+ coeffs = [1.0 , 2.0 , 3.0 , 4.0 , 1.0 ]
61+ A_true = np .polynomial .polynomial .polycompanion (coeffs )
62+ A_true = np .fliplr (np .rot90 (A_true )).T
63+ B_true = np .matrix ("1.0 1.0 1.0 1.0" ).T
64+ C_true = np .matrix ("1.0 0.0 0.0 0.0" )
65+ D_true = 42.0
66+
67+ # Perform a coordinate transform with a random invertible matrix
68+ T_true = np .matrix ([[- 0.27144004 , - 0.39933167 , 0.75634684 , 0.44135471 ],
69+ [- 0.74855725 , - 0.39136285 , - 0.18142339 , - 0.50356997 ],
70+ [- 0.40688007 , 0.81416369 , 0.38002113 , - 0.16483334 ],
71+ [- 0.44769516 , 0.15654653 , - 0.50060858 , 0.72419146 ]])
72+
73+ A = np .linalg .solve (T_true , A_true )* T_true
74+ B = np .linalg .solve (T_true , B_true )
75+ C = C_true * T_true
76+ D = D_true
77+
78+ # Create a state space system and convert it to the observable canonical form
79+ sys_check , T_check = canonical_form (ss (A , B , C , D ), "observable" )
80+
81+ # Check against the true values
82+ np .testing .assert_array_almost_equal (sys_check .A , A_true )
83+ np .testing .assert_array_almost_equal (sys_check .B , B_true )
84+ np .testing .assert_array_almost_equal (sys_check .C , C_true )
85+ np .testing .assert_array_almost_equal (sys_check .D , D_true )
86+ np .testing .assert_array_almost_equal (T_check , T_true )
87+
88+ def test_unobservable_system (self ):
89+ """Test observable canonical form with an unobservable system"""
90+
91+ # Create an observable system
92+ A = np .matrix ("1.0 2.0 2.0; 4.0 5.0 5.0; 7.0 8.0 8.0" )
93+ B = np .matrix ("1.0 1.0 1.0" ).T
94+ C = np .matrix ("1.0 1.0 1.0" )
95+ D = 42.0
96+ sys = ss (A , B , C , D )
97+
98+ # Check if an exception is raised
99+ np .testing .assert_raises (ValueError , canonical_form , sys , "observable" )
100+
101+ if __name__ == '__main__' :
102+ unittest .main ()
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