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dc.contributor.authorBall, Joseph A.en_US
dc.contributor.authorGroenewald, Gilbert J.
dc.contributor.authorTer Horst, Sanne
dc.contributor.authorFang, Quanlei
dc.identifier.citationBall, J.A. et al. 2009. Equivalence of robust stabilization and robust performance via feedback. Mathematics of control signals and systems, 21(1):51-68, Jan.[]en_US
dc.identifier.issn1435-568X (Online)
dc.description.abstractOne approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified L2-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to linear matrix inequality conditions
dc.subjectMultidimensional linear systems
dc.subjectOutput feedback
dc.subjectRobust stabilization
dc.subjectRobust performance
dc.subjectLinear fractional transformations
dc.subjectLinear matrix inequalities
dc.titleEquivalence of robust stabilization and robust performance via feedbacken_US
dc.contributor.researchID24116327 - Ter Horst, Sanne
dc.contributor.researchID12066680 - Groenewald, Gilbert Joseph

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