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Insensitivity of a class of LQ regulators of neutral systems
Author(s) -
Kubo Tomohiro
Publication year - 2004
Publication title -
electrical engineering in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.136
H-Index - 28
eISSN - 1520-6416
pISSN - 0424-7760
DOI - 10.1002/eej.20013
Subject(s) - sensitivity (control systems) , mathematics , control theory (sociology) , quadratic equation , linear system , linear quadratic regulator , function (biology) , class (philosophy) , regulator , matrix (chemical analysis) , topology (electrical circuits) , mathematical analysis , mathematical optimization , computer science , engineering , combinatorics , optimal control , biochemistry , chemistry , materials science , geometry , control (management) , artificial intelligence , electronic engineering , evolutionary biology , gene , composite material , biology
It is well known that the linear quadratic regulators of finite dimensional linear systems have the insensitivity property. In this paper, as a particular class of infinite dimensional systems, a neutral delay‐differential system is considered as a plant. A class of linear quadratic regulators is constructed for the plant using a simple feedback law, which does not require real‐time either integral or derivative operations. The feedback gain is calculated by solving a finite dimensional linear matrix inequality. First, it is shown that the regulator satisfies the circle condition. Then, its sensitivity against the parameter variations is evaluated. In the single‐input case, it is done by calculating the absolute value of the sensitivity function. In the multi‐input case, it is done by the so‐called “comparison sensitivity” method where the sensitivities of the closed‐loop system and the open‐loop system are compared based on certain sensitivity indices. Procedures used for the investigation of the regulator's properties are based on natural extension of methods proposed by Perkins and Cruz for the finite dimensional case. As a result, it is found that the class of linear quadratic regulators of neutral systems, similarly to finite dimensional systems, has the insensitivity property. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(2): 28–34, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20013