| 依赖延迟线性时滞系统的稳定性判据 |
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| 引用本文： | 朱莹, 高其娜, 肖扬. 依赖延迟线性时滞系统的稳定性判据. 自动化学报, 2013, 39(12): 2150-2153. doi: 10.3724/SP.J.1004.2013.02150 |
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| 作者姓名： | 朱莹 高其娜 肖扬 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金（60572093）资助，国防科研课题（102476）资助 |
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| 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.
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| 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 |
| 收稿时间： | 2012-04-01 |
| 修稿时间： | 2012-09-19 |
Stability Criteria of Linear Time-delay Systems with Dependent Delays |
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| ZHU Ying, GAO Qi-Na, XIAO Yang. Stability Criteria of Linear Time-delay Systems with Dependent Delays. ACTA AUTOMATICA SINICA, 2013, 39(12): 2150-2153. doi: 10.3724/SP.J.1004.2013.02150 |
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| Authors: | ZHU Ying GAO Qi-Na XIAO Yang |
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| Affiliation: | 1. School of Electronic and Information Engineering, Beihang University, Beijing 100191;;;2. Beijing Aeronautical Technology Research Center, Beijing 100076;;;3. School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044 |
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| Abstract: | 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 characteristic polynomials of LTD-DD systems belong to quasipolynomials, 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 hybrid 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 algorithms. |
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| Keywords: | Control theory time-delay systems quasipolynomials two-dimensional polynomials stability criteria |
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