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Optimal, constant I/O similarity scaling for full-information and state- feedback control problems. (English) Zbl 0772.49021
The paper discusses the optimal constant scaling problem of full- information \(H_ \infty\) control. The problem arises, because it is impossible to capture all robustness and performance in a single \(H_ \infty\) norm cost function. Alternatively, diagonal similarity scalings of certain closed loop transfer functions can be used. The set of allowable diagonal scalings is problem dependent. The scaling set considered in the paper is a prescribed convex set of positive definite matrices.
The solution to the posed problem is obtained by transforming the original problem into a convex feasibility problem, specifically, a structured, linear matrix inequality. In special cases, solvability of the full-information problem is equivalent to solvability of the state- feedback problem. The paper concludes with a numerical example.
Reviewer: H.Koivo (Tampere)

MSC:
90C25 Convex programming
93B35 Sensitivity (robustness)
Software:
QDES
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