Worst‐case stability and performance with mixed parametric and dynamic uncertainties

Summary This work deals with computing the worst‐case stability and the worst‐case H∞ performance of linear time‐invariant systems subject to mixed real‐parametric and complex‐dynamic uncertainties in a compact parameter set. Our novel algorithmic approach is tailored to the properties of the nonsmo...

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Bibliographic Details
Published in:International journal of robust and nonlinear control 2017-05, Vol.27 (8), p.1284-1301
Main Authors: Apkarian, Pierre, Noll, Dominikus
Format: Article
Language:English
Subjects:
Algorithms
Computation
Computer Science
Dynamic stability
dynamic uncertainties
Dynamical systems
H-infinity control
Lower bounds
Nonlinear dynamics
Nonlinearity
nonsmooth optimization
Optimization
Parameter uncertainty
parametric uncertainties
robustness analysis
Stability
Uncertainty
Upper bounds
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Summary:Summary This work deals with computing the worst‐case stability and the worst‐case H∞ performance of linear time‐invariant systems subject to mixed real‐parametric and complex‐dynamic uncertainties in a compact parameter set. Our novel algorithmic approach is tailored to the properties of the nonsmooth worst‐case functions associated with stability and performance, and this leads to a fast and reliable optimization method, which finds good lower bounds of μ. We justify our approach theoretically by proving a local convergence certificate. Because computing μ is known to be NP‐hard, our technique should be used in tandem with a classical μ upper bound to assess global optimality. Extensive testing indicates that the technique is practically attractive. Copyright © 2016 John Wiley & Sons, Ltd.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.3628