Extracting coefficient Matrix and vector from available polynomial Expressions with exponential terms

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Rajani Metri 2019-5-12

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评论： Star Strider 2021-3-25

Hello All,

I have stuck in one problem, where I have variable matrix vector available and I want to extract the coefficient matrix and variable vector from that original polynomial vector matrix. For e.g. if A is matrix as:

and I want to extract its coefficients and variable vector as given below:

So my question is how to compute or Extract Matrix Y and Matrix Z from A which comprises of expressions with exponential terms of eigenvalues of system matrix.

Is there any direct command? I tried commands like - coeffs, sysvar, equationsToMatrix but in all those cases the variables are fixed.

So, please help me in solving this above problem.

Thank You.

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采纳的回答

Star Strider 2019-5-12

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You have not shown what you already tried or what the results were.

In R2019a, this is possible with a for loop (since coeffs apparently doesn’t like matrices):

syms lambda1 lambda2 t 
A = [exp(-lambda1*t)+3*exp(-lambda2*t); -2*exp(-lambda1*t)+4*exp(-lambda2*t)];
for k = 1:size(A,1)
    [Ac{k},trm{k}] = coeffs(A(k,:));
end
Cfs = [Ac{1}; Ac{2}]
Trm = [trm{1}; trm{2}]

producing:

Cfs =
[  1, 3]
[ -2, 4]
Trm =
[ exp(-lambda1*t), exp(-lambda2*t)]
[ exp(-lambda1*t), exp(-lambda2*t)]

That may be the best you can hope for.

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Rajani Metri 2019-5-12

Hello,

I have tried those (coeffs, sysvar, equationsToMatrix) commands, but it showed error.

Sorry that I have not mentioned how A is calculated in my question. Actually A matrix is multiplication of State Transistion Matrix (STM) and column input vector B of state space. So here we are not defining A, but it is computed by MATLAB only (STM*B). So everytime System matrix changes, then STM changes, so as Lymbda values.

As in your answer you have shown that A is defined and lymbda are taken as 'syms', but after calculation of STM*B those values may change, we don't know depending upon the System Matrix and Input Matrix of State Space. In such cases how we can find? It should be applicable to generalised system.

For e.g. First example have lyambdas as -1 and -0.5. And I want to MATLAB to extract Y and Z matrices from A1.