Book Section records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 13:20:01 +0000Model reduction of LFT systems
https://resolver.caltech.edu/CaltechAUTHORS:20190319-091249008
Authors: {'items': [{'id': 'Wang-Weizheng', 'name': {'family': 'Wang', 'given': 'Weizheng'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John'}, 'orcid': '0000-0002-1828-2486'}, {'id': 'Beck-C-L', 'name': {'family': 'Beck', 'given': 'Carolyn'}}, {'id': 'Glover-K', 'name': {'family': 'Glover', 'given': 'Keith'}}]}
Year: 1991
DOI: 10.1109/CDC.1991.261574
The notion of balanced realizations and balanced truncation model reduction, including guaranteed error bounds, is extended to general Q-stable linear fractional transformations (LFTs). Since both multidimensional and uncertain systems are naturally represented using LFTs, this can be interpreted either as doing state order reduction for multidimensional systems or as uncertainty simplification in the case of uncertain systems. The role of Lyapunov equations in the 1D theory is replaced by linear matrix inequalities (LMIs). All proofs are given in detail as they are very short and greatly simplify even the standard 1D case.https://authors.library.caltech.edu/records/5vm66-4ns37Mixed µ upper bound computation
https://resolver.caltech.edu/CaltechAUTHORS:20190319-085951997
Authors: {'items': [{'id': 'Beck-C-L', 'name': {'family': 'Beck', 'given': 'Carolyn'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John'}, 'orcid': '0000-0002-1828-2486'}]}
Year: 1992
DOI: 10.1109/CDC.1992.371241
Computation of the mixed real and complex µ upper bound expressed in terms of linear matrix inequalities (LMIs) is considered. Two existing methods are used, the Osborne (1960) method for balancing matrices, and the method of centers as proposed by Boyd and El Ghaoui (1991). These methods are compared, and a hybrid algorithm that combines the best features of each is proposed. Numerical experiments suggest that this hybrid algorithm provides an efficient method to compute the upper bound for mixed µ.https://authors.library.caltech.edu/records/4arn5-jkd26Model reduction of behavioural systems
https://resolver.caltech.edu/CaltechAUTHORS:20190320-142555896
Authors: {'items': [{'id': 'Beck-C-L', 'name': {'family': 'Beck', 'given': 'Carolyn'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John'}, 'orcid': '0000-0002-1828-2486'}]}
Year: 1993
DOI: 10.1109/CDC.1993.325889
We consider model reduction of uncertain behavioural models. Machinery for gap-metric model reduction and multidimensional model reduction using linear matrix inequalities is extended to these behavioural models. The goal is a systematic method for reducing the complexity of uncertain components in hierarchically developed models which approximates the behavior of the full-order system. This paper focuses on component model reduction that preserves stability under interconnection.https://authors.library.caltech.edu/records/wcwj4-za217Reducing uncertain systems and behaviors
https://resolver.caltech.edu/CaltechAUTHORS:20190315-144945947
Authors: {'items': [{'id': 'Beck-C-L', 'name': {'family': 'Beck', 'given': 'Carolyn'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John'}, 'orcid': '0000-0002-1828-2486'}]}
Year: 1996
DOI: 10.1109/CDC.1996.574435
This paper considers the problem of reducing the dimension of a model for an uncertain system whilst bounding the resulting error. Model reduction methods with guaranteed upper error bounds have previously been established for uncertain systems described by a state-space type realization; specifically, by a linear fractional transformation (LFT) of a constant realization matrix over a structured uncertainty operator. In contrast to traditional 1-D model reduction where upper bounds on reduction are matched with comparable lower bounds, in the uncertain system problem there have previously been no lower bounds established. The computation of both upper and lower bounds is discussed in this paper, including a discussion of the use of Hankel-like matrices. These model reduction methods and error bound computations are then discussed in the context of kernel representations of behavioral uncertain systems.https://authors.library.caltech.edu/records/db3tb-xbk76