Find non singular transformation matrix

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RJS 2021-11-17

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https://ww2.mathworks.cn/matlabcentral/answers/1588879-find-non-singular-transformation-matrix

评论： Paul 2021-12-22

I am working on state space system in matlab script. here C =[0 0 0 0 0 0 1 0 1 0] but I want to observe 1st state i.e. required Cr = [1 0 0 0 0 0 0 0 0 0]. So to get this C I am using transformation matrix T = Cr/C.....but here i am getting singular T matrix

I want nonsingular T matrix

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Paul 2021-11-17

To make sure we're clear on the question:

You have a model

xdot = A*x + B*u

y = C*x + D*u

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

The goal is find the similarity tranformation matrix T that defines a new state vector, z, so that

zdot = Anew*z + Bnew*u

y = Cnew*z + Dnew*u

where Cnew = [1 0 0 0 0 0 0 0 0 0]

Is my understanding correct?

RJS 2021-11-18

yes

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采纳的回答

Paul 2021-11-17

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https://ww2.mathworks.cn/matlabcentral/answers/1588879-find-non-singular-transformation-matrix#answer_834044

编辑：Paul 2021-11-17

在 MATLAB Online 中打开

Assuming the goal is as described in this comment, one solution would be:

T1 = [0 0 0 0 0 0 1 0 1 0];
T = [T1;null(T1).']; 

See this Answer thread for much more discussion and other approaches.

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RJS 2021-12-22

If the required C vector is [0 0 0 0 1 0 0 0 0 0], then how to find this transformation

Paul 2021-12-22

在 MATLAB Online 中打开

Follow the same approach, but put the C vector from plant in the fifth row of T instead of the first. Here's an example:

sys = rss(10); % random system for example
sys.c
ans = 1×10
   -0.2270   -1.7085         0   -1.4590    0.2800    0.3869    1.1516   -0.3147         0   -0.6773
N = null(sys.c).';
T = [N(1:4,:); sys.c; N(5:end,:)]; % sys.c in the fifth row, distribute N across the others
sysnew = ss2ss(sys,T);
sysnew.c  % verify desired result
ans = 1×10
     0     0     0     0     1     0     0     0     0     0