依赖延迟线性时滞系统的稳定性判据  

Stability Criteria of Linear Time-delay Systems with Dependent Delays

作　　者：朱莹[1,2] 高其娜[1,2] 肖扬[3] 

机构地区：[1]北京航空航天大学电子与信息工程学院,北京100191 [2]北京航空技术研究中心北京100076 [3]北京交通大学计算机与信息技术学院北京100044

出　　处：《自动化学报》2013年第12期2150-2153,共4页Acta Automatica Sinica

基　　金：国家自然科学基金(60572093)资助;国防科研课题(102476)资助~~

摘　　要：由于独立延迟线性时滞(Linear time-delay with independent delays,LTD-ID)系统的稳定条件对系统参数有严格的限制,只有极少数依赖延迟线性时滞(LTD with dependent delays,LTD-DD)系统可满足该稳定条件.LTD-ID系统的特征多项式属拟多项式,其根为多重延迟的函数,这使得LTD-ID系统的稳定性检验非常困难.为解决该问题,基于二维域混合多项式,本文提出LTD-DD系统的若干稳定性判据.应用例表明所提出的稳定性判据是简单的和有效的,所提出的定理4可解决现有LMI稳定性判据的保守性问题.This paper reveals that only fewer of the linear time- delay （LTD） systems with dependent delays （LTD-DD systems） can satisfy the stability condition for linear time-delay systems with independent delays （LTD-ID systems）, since there is a strict limitation for the parameters of the LTD-DD systems. The char- acteristic polynomials of LTD-DD systems belong to quasipoly- nomials, and the roots of the quasipolynomials are the function of the multiple delays, which make the stability test of LTD- DD systems difficult. To solve the problem, based on 2-D hy- brid polynomials, some stability criteria of LTD-DD systems are proposed. Examples show that the proposed stability criteria are simple and valid, and that the proposed theorem can solve the conservatism problem of existing LMI stability testing algo- rithms.

关 键 词：控制理论 时滞系统 拟多项式 二维多项式 稳定性判据 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]