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SVD controllers for H_2-, H_-∞ and μ-optimal control
Morten Hovd, Richard D. Braatz and Sigurd Skogestad

Automatica
33 (3), pp 433-439

Abstract

Plant structure is utilized for the simplification of system analysis and controller synthesis. For plants where the directionality is independent of frequency, the singular-value decomposition (SVD) is used to decouple the system into nominally independent subsystems of lower dimension. In H₂- and H∞-optimal control, the controller synthesis can then be performed for each of these subsystems independently, and the resulting overall SVD controller will be optimal (the same will hold for any norm that is invariant under unitary transformations). In H∞-optimal control the resulting controller is also super-optimal, since a controller of dimension n × n will minimize the norm in n directions. For robust control in terms of the structured singular value μ, the SVD controller is optimal for a practically relevant class of block-diagonal structures and uncertainty and performance weights.