LMI
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i would like to ask how to obtain the matrix E, which satisfy the following constrain,
E * [x]' >=0
I need the matrix E for stability analysis of piecewise linear system.
but not sure how to find this. if anyone knows plz help me out.
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Answers (1)
Walter Roberson
on 29 Jun 2011
Are you sure you don't mean
[x] * E * [x]' >= 0
If you do then E would be an example of a positive semi-definite matrix. Such matrices are not unique.
To generate an N x N positive semi-definite matrix, you can use
t = rand(N,N);
E = t' * t;
and E will now be positive semi-definite.
If the above is not what you mean, then E would have to be a column vector and [x]' would have to be a row vector. If the values of x are not fixed in advance, then the only solution is that E is the all-zero vector. There may be other solutions if the permissible values of x are bounded.
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Walter Roberson
on 1 Jul 2011
Another question: >= 0 implies the result is a scalar, but your reference to "not necessarily be symmetric" implies a matrix result. Do you mean that each element of a resulting matrix E*x' is >= 0, or do you mean that E*x' is going to be a vector and each element of the vector will be >=0, or do you mean the result will be a scalar that will be >=0 ?
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