Stability Radius
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The stability radius of a continuous function f (in a functional space F) with respect to an open stability domain D is the distance between f and the set of unstable functions (with respect to D). We say that a function is stable with respect to D if its spectrum is in D. Here, the notion of spectrum is defined on a case by case basis, as explained below.The notion of stability radius is generally applied to special functions as polynomials (the spectrum is then the ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The stability radius of a continuous function f (in a functional space F) with respect to an open stability domain D is the distance between f and the set of unstable functions (with respect to D). We say that a function is stable with respect to D if its spectrum is in D. Here, the notion of spectrum is defined on a case by case basis, as explained below.The notion of stability radius is generally applied to special functions as polynomials (the spectrum is then the roots) and matrices (the spectrum is the eigenvalues). The case where C is a proper subset of F permits us to consider structured perturbations (e.g. for a matrix, we could only need perturbations on the last row). It is an interesting measure of robustness, for example in control theory.
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