@@ -52,3 +52,47 @@ def test_unreachable_system(self):
5252
5353# Check if an exception is raised
5454np .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 .flipud (A_true ))
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+ A = np .linalg .solve (T_true ,A_true )* T_true
73+ B = np .linalg .solve (T_true ,B_true )
74+ C = C_true * T_true
75+ D = D_true
76+
77+ # Create a state space system and convert it to the observable canonical form
78+ sys_check ,T_check = canonical_form (ss (A ,B ,C ,D ),"observable" )
79+
80+ # Check against the true values
81+ np .testing .assert_array_almost_equal (sys_check .A ,A_true )
82+ np .testing .assert_array_almost_equal (sys_check .B ,B_true )
83+ np .testing .assert_array_almost_equal (sys_check .C ,C_true )
84+ np .testing .assert_array_almost_equal (sys_check .D ,D_true )
85+ np .testing .assert_array_almost_equal (T_check ,T_true )
86+
87+ def test_unobservable_system (self ):
88+ """Test observable canonical form with an unobservable system"""
89+
90+ # Create an unobservable system
91+ A = np .matrix ("1.0 2.0 2.0; 4.0 5.0 5.0; 7.0 8.0 8.0" )
92+ B = np .matrix ("1.0 1.0 1.0" ).T
93+ C = np .matrix ("1.0 1.0 1.0" )
94+ D = 42.0
95+ sys = ss (A ,B ,C ,D )
96+
97+ # Check if an exception is raised
98+ np .testing .assert_raises (ValueError ,canonical_form ,sys ,"observable" )