Generalized X-Y Functions, the Linear Matrix Inequality, and Triangular Factorization for Linear Control Problems

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/695 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/695 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/695 archive 351 disk0/00/00/06/74 2016-01-15 01:43:54 2021-08-27 17:08:32 2016-01-15 01:43:54 monograph show 2 Casti J.L. 974 Generalized X-Y Functions, the Linear Matrix Inequality, and Triangular Factorization for Linear Control Problems pub iis_met prog_sds The relationship between the linear matrix inequality (LMI), generalized X-Y functions, and triangular factorization is examined within the framework of the classical linear-quadratic-gaussian problem. It is shown that the generalized X-Y functions arise naturally as components within the factors of the matrix forming the LMI when that matrix is decomposed into its symmetric triangular factors. This viewpoint enables us to propose a low-dimensional computational algorithm for time-dependent problems which reduces to the generalized X-Y situation for constant systems. In addition to the basic factorization results, we also briefly touch upon several related topics including the infinite-interval (regulator) problem, singular control problems, canonical forms, and numerical considerations. 1976-02 published RM-76-010 RM-76-010 10 1179 public research_memorandum IIASA, Laxenburg, Austria 15 FALSE info:eu-repo/semantics/book