[
    {
        "id": "authors:db3tb-xbk76",
        "collection": "authors",
        "collection_id": "db3tb-xbk76",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190315-144945947",
        "type": "book_section",
        "title": "Reducing uncertain systems and behaviors",
        "book_title": "Proceedings of 35th IEEE Conference on Decision and Control",
        "author": [
            {
                "family_name": "Beck",
                "given_name": "Carolyn",
                "clpid": "Beck-C-L"
            },
            {
                "family_name": "Doyle",
                "given_name": "John",
                "orcid": "0000-0002-1828-2486",
                "clpid": "Doyle-J-C"
            }
        ],
        "abstract": "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.",
        "doi": "10.1109/CDC.1996.574435",
        "isbn": "0-7803-3590-2",
        "publisher": "IEEE",
        "place_of_publication": "Piscataway, NJ",
        "publication_date": "1996-12",
        "pages": "712-714"
    },
    {
        "id": "authors:wcwj4-za217",
        "collection": "authors",
        "collection_id": "wcwj4-za217",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190320-142555896",
        "type": "book_section",
        "title": "Model reduction of behavioural systems",
        "book_title": "Proceedings of 32nd IEEE Conference on Decision and Control",
        "author": [
            {
                "family_name": "Beck",
                "given_name": "Carolyn",
                "clpid": "Beck-C-L"
            },
            {
                "family_name": "Doyle",
                "given_name": "John",
                "orcid": "0000-0002-1828-2486",
                "clpid": "Doyle-J-C"
            }
        ],
        "abstract": "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.",
        "doi": "10.1109/CDC.1993.325889",
        "isbn": "0-7803-1298-8",
        "publisher": "IEEE",
        "place_of_publication": "Piscataway, NJ",
        "publication_date": "1993-12",
        "pages": "3652-3657"
    },
    {
        "id": "authors:4arn5-jkd26",
        "collection": "authors",
        "collection_id": "4arn5-jkd26",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190319-085951997",
        "type": "book_section",
        "title": "Mixed \u00b5 upper bound computation",
        "book_title": "Proceedings of the 31st IEEE Conference on Decision and Control",
        "author": [
            {
                "family_name": "Beck",
                "given_name": "Carolyn",
                "clpid": "Beck-C-L"
            },
            {
                "family_name": "Doyle",
                "given_name": "John",
                "orcid": "0000-0002-1828-2486",
                "clpid": "Doyle-J-C"
            }
        ],
        "abstract": "Computation of the mixed real and complex \u00b5 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 \u00b5.",
        "doi": "10.1109/CDC.1992.371241",
        "isbn": "0-7803-0872-7",
        "publisher": "IEEE",
        "place_of_publication": "Piscataway, NJ",
        "publication_date": "1992-12",
        "pages": "3187-3192"
    },
    {
        "id": "authors:5vm66-4ns37",
        "collection": "authors",
        "collection_id": "5vm66-4ns37",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190319-091249008",
        "type": "book_section",
        "title": "Model reduction of LFT systems",
        "book_title": "Proceedings of the 30th IEEE Conference on Decision and Control",
        "author": [
            {
                "family_name": "Wang",
                "given_name": "Weizheng",
                "clpid": "Wang-Weizheng"
            },
            {
                "family_name": "Doyle",
                "given_name": "John",
                "orcid": "0000-0002-1828-2486",
                "clpid": "Doyle-J-C"
            },
            {
                "family_name": "Beck",
                "given_name": "Carolyn",
                "clpid": "Beck-C-L"
            },
            {
                "family_name": "Glover",
                "given_name": "Keith",
                "clpid": "Glover-K"
            }
        ],
        "abstract": "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.",
        "doi": "10.1109/CDC.1991.261574",
        "isbn": "0-7803-0450-0",
        "publisher": "IEEE",
        "place_of_publication": "Piscataway, NJ",
        "publication_date": "1991-12",
        "pages": "1233-1238"
    }
]