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

Casti JL (1976). Generalized X-Y Functions, the Linear Matrix Inequality, and Triangular Factorization for Linear Control Problems. IIASA Research Memorandum. IIASA, Laxenburg, Austria: RM-76-010

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Abstract

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.

Item Type: Monograph (IIASA Research Memorandum)
Research Programs: System and Decision Sciences - Core (SDS)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 01:43
Last Modified: 22 Jul 2016 09:38
URI: http://pure.iiasa.ac.at/674

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