Insensitivity of a Class of LQ Regulators of Neutral Systems

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  • Kubo Tomohiro
    Dept. of Electrical and Electronic Engineering, University of Tokushima

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  • 中立系におけるあるクラスの最適レギュレータの低感度特性
  • チュウリツケイ ニ オケル アル クラス ノ サイテキ レギュレータ ノ テイカンド トクセイ

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Abstract

It is well known that the linear quadratic regulator of finite dimensional linear systems has the insensitivity property. In this paper, as a particular class of infinite dimensional linear systems, a neutral delay-differential system is considered as a plant. A class of linear quadratic regulators is constructed for the plant via a simple feedback law without real-time integral nor derivative operation. The feedback gain is calculated with a solution of a finite dimensional linear matrix inequality. First, it is shown that the regulator satisfies the circle condition. Then, its sensitivity against the parameter variation 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 method so called “comparison sensitivity”, where the sensitivities of the closed loop system and the open loop system are compared by some sensitivity indices.The procedure to investigate the property is a natural extension of one by Perkins and Cruz, where the finite dimensional case was treated. As a result, it is shown that the class of linear quadratic regulators of neutral systems has the insensitivity property as well as that of finite dimensional systems.

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