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Notes on \(\mu \) and \(\ell _1\) robustness tests. (English) Zbl 1274.93218
Summary: An upper bound for the complex structured singular value related to a linear time-invariant system over all frequencies is given. It is in the form of the spectral radius of the \(\mathcal {H}_{\infty }\)-norm matrix of SISO input-output channels of the system when uncertainty blocks are SISO. In the case of MIMO uncertainty blocks; the upper bound is the \(\infty \)-norm of a special non-negative matrix derived from \(\mathcal {H}_{\infty }\)-norms of SISO channels of the system. The upper bound is fit into the inequality relation between the results of \(\mu \) and \(\ell _1\) robustness tests.
93D09 Robust stability
93C35 Multivariable systems, multidimensional control systems
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