Structure of stability and asymptotic stability sets of families of linear differential systems with parameter multiplying the derivative: II |
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Authors: | E A Barabanov |
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Institution: | 1.Institute for Mathematics,National Academy of Sciences,Minsk,Belarus |
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Abstract: | We consider families of linear differential systems depending on a real parameter that occurs only as a factor multiplying
the matrix of the system. The asymptotic stability set of such a family is defined as the set of all parameter values for
which the corresponding systems in the family are asymptotically stable. We prove that a set on the real axis is the asymptotic
stability set of such a family if and only if it is an F
σδ
-set lying entirely on an open ray with origin at zero. In addition, for any set of this kind, the coefficient matrix of a
family whose asymptotic stability set coincides with this set can be chosen to be infinitely differentiable and uniformly
bounded on the time half-line. |
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Keywords: | |
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