MIMO control system with marginally stable poles at the origin

hello everyboday

I have a mimo system trying to design a controller for it, when I test the pole zero locations it tells that all are in the lefet side of the pole zero s-plane and the pole values are negative, but the problem the poles and the zeros are very neer to the origin only one is to far from them with negative value also.

the system has been tested with the impulse responce and it ossilate to zero

the system is 3 inputs and 3 outputs, with 5 states

can anybody give a idea how to reblace the pole locations to get a good gain value for the control designe?

A = [0	0	-2244.38902743142	0	0
0	0	810.810810810811	-1351.35135135135	0
29508.1967213115	-19672.1311475410	-1.87692307692308e-06	0	0
0	222222.222222222	0	-4444444.44444444	0
0	0	0	0	0];

B = [124688.279301746	124688.279301746	-1.90000000000000
0	-67567.5675675676	1283.78378378378
-2.56000000000000	-4.25800000000000	0
0	0	0
0	0	-111770.491803279];

C = [0	0	1	0	0
0	0	0	1	0
0	0	0	0	1]

D = [0	0	0
   0	0	0
0	0	0 ]

please anybody have an idea how to desin a controller.

thank you

Answer 1

[M]

How do you test the pole zero locations ?

Here, you have a pole equal to 0.

[Mohamed]

I use the eig() command and it gives me negative value poles

[M]

Well, eig(A) should return a value equals to zero, as the last line of matrix A is full of zero