Ch Control System Toolkit Demos
Example 4 -- Controllability and Observability

The linearized equations of motion for a satellite are

. X = AX + BU Y = CX + DU where [0 1 0 0 ] [0 0] A =[0 0 0 0.0024], B = [1 0], C = [1 0 0 0], D = 0 [0 0 0 1 ] [0 0] [0 0 1 0] [0 0.0024 0 0 ] [0 1] determine the controllability and observability of the system.

Answer:
The controllability matrix is

        [0 0 1         0        0         0.002400  -0.000006 0        ] 
   co = [1 0 0         0.002400 -0.000006 0         0         0        ]
        [0 0 0         1        -0.002400 0         0         -0.000006]
        [0 1 -0.002400 0        0         -0.000006 0         0        ]
The observability matrix is
        [1 0         0 0        ]
        [0 0         1 0        ]
        [0 1         0 0        ]
   ob = [0 0         0 1        ]
        [0 0         0 0.002400 ]
        [0 -0.002400 0 0        ]
        [0 -0.000006 0 0        ]
        [0 0         0 -0.000006]

Program in Ch
Output in Ch
Program in MATLAB