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The complex structured singular value. (English) Zbl 0772.93023

Summary: A tutorial introduction to the complex structured singular value \((\mu)\) is presented, with an emphasis on the mathematical aspects of \(\mu\). The \(\mu\)-based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems. Several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared, and a simple synthesis problem is studied. Uncertain systems are represented using Linear Fractional Transformations (LFTs) which naturally unify the frequency-domain and state space methods.

MSC:

93B35 Sensitivity (robustness)
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
93C73 Perturbations in control/observation systems
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