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Mixed-sensitivity optimization for a class of unstable infinite- dimensional systems. (English) Zbl 0776.93023

Summary: We solve the \(H^ \infty\) mixed-sensitivity minimization problem for a class of unstable distributed systems. The solution is based on an extension of the skew Toeplitz methodology. The key mathematical fact used is that the skew Toeplitz operators arising in the unstable case are finite-rank perturbations of the classical skew Toeplitz operators obtained from compressions of rational functions. A system of linear equations (the singular system) is derived for this class of operators, from which one can compute the associated singular values and vectors. An example is included to illustrate the results.

MSC:

93B35 Sensitivity (robustness)
93B36 \(H^\infty\)-control
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