2002 · 81 citations · 10 references
EngineeringMathematicsSystems EngineeringDynamical SystemsModel-based Systems EngineeringSystems ModelingApproximation AlgorithmsControl TheoryNumerical StabilityReduced-order ModelingStability TheoryState-space ModelingBalanced TruncationError BoundsLinear ApproximationLinear Stability AnalysisLower Bounds Of ErrorStability Analysis Of Linear Systems
Two well known LTI approximation methods-balanced truncation and optimal Hankel norm approximation-are extended to the LPV framework. Quadratic stability of the approximants and generalisations of known LTI error bounds are examined. The concept of the graph operator of an LPV system is discussed. We show how, by approximating the graph operator, the state-dimension of models that are not quadratically stable may be reduced.
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