Abstract
Given a matrix M ∈ Сn×n and a set of positive integers χ = (k 1,⋯,k m) with k 1+⋯+k m = n, the so-called complex structured singular value µχ(M), (complex µ for short), is defined as follows:
where
Let \(\hat{\mu }\) be an approximation of µ. We call \(\hat{\mu }\) an r-approximation, r > 0, if either
or
Note that \(\hat{\mu }\) {a_o} \approx {c_o} \approx \sqrt {2{a_c}} ,{b_o} \approx {a_c} is an upper bound in the former case and an lower bound in the latter.
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© 1999 Springer-Verlag London Limited
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Fu, M. (1999). Approximation of complex µ . In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_22
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DOI: https://doi.org/10.1007/978-1-4471-0807-8_22
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