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A new characterization of invariant subspaces of \(H^{2}\) and applications to the optimal sensitivity problem. (English) Zbl 1129.93375

Summary: This paper gives a new equivalent characterization for invariant subspaces of \(H^{2}\), when the underlying structure is specified by the so-called pseudorational transfer functions. This plays a fundamental role in computing the optimal sensitivity for a certain important class of infinite-dimensional systems, including delay systems. A closed formula, easier to compute than the well-known Zhou–Khargonekar formula, is given for optimal sensitivity for such systems. An example is given to illustrate the result.

MSC:

93B36 \(H^\infty\)-control
46E15 Banach spaces of continuous, differentiable or analytic functions
47A15 Invariant subspaces of linear operators
93B35 Sensitivity (robustness)
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