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Content Provider | IEEE Xplore Digital Library |
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Author | Latchman, H. A. Norris, R. J. |
Copyright Year | 1990 |
Description | Author affiliation: Department of Electrical Engineering, University of Florida, Gainesville Florida 32611 (Latchman, H. A.; Norris, R. J.) |
Abstract | Optimal scaling techniques have become widely accepted tools in the analysis and design of systems in the presence of structured uncertainties. Among these are the block similarity scaling techniques, the so-called "structured singular value" introduced by Doyle, which has been shown to apply to general block structured uncertainties. For the special case of an n × n uncertainty matrix with $n^{2}$ nonzero 1 × 1 blocks, the structured singular value technique with similarity scaling suffers from the disadvantage of having to expand an n × n matrix problem to an $n^{2}$ × $n^{2}$ matrix optimization problem with $n^{2}$ - 1 free variables. For this same class of uncertainties with scalar blocks, an alternative approach proposed by Kouvaritakis and Latchman employs a "nonsimilarity" scaling technique which preserves the original matrix dimension (n × n) and requires only 2(n - l) optimization parameters. The aim of this paper is to show that for scalar block structured uncertainties, the structure of the problem may be exploited to yield a similarity scaling method which uses no more than 2(n - 1) rather than $n^{2}$ - 1 optimization parameters. A simple extension of this result shows that a reduction in the number of free variables is also possible for general block structured uncertainties. A more efficient implementation of the vector optimization method developed by Fan and Tits is also proposed. Several examples are included to illustrate the results. |
Starting Page | 2058 |
Ending Page | 2062 |
File Size | 405520 |
Page Count | 5 |
File Format | |
Language | English |
Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Publisher Date | 1990-05-23 |
Publisher Place | USA |
Access Restriction | Subscribed |
Rights Holder | American Automatic Control Council(AACC) |
Subject Keyword | Uncertainty Optimization methods Stability Frequency dependence Convergence Terminology Design optimization MIMO Frequency measurement Matrix converters |
Content Type | Text |
Resource Type | Article |
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