A Convex Characterization of Robust Stability for Positive and Positively Dominated Linear Systems

Marcello Colombino; Roy S. Smith

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A Convex Characterization of Robust Stability for Positive and Positively Dominated Linear Systems

机译：正和正控制线性系统的鲁棒稳定性的凸刻画

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We provide convex necessary and sufficient conditions for the robust stability of linear positively dominated systems. In particular, we show that the structured singular value is always equal to its convex upper bound for nonnegative matrices and we use this result to derive necessary and sufficient Linear Matrix Inequality (LMI) conditions for robust stability that involve only the system's static gain. We show how this approach can be applied to test the robust stability of the Foschini–Miljanic algorithm for power control in wireless networks in presence of uncertain interference.

机译：我们为线性正控制系统的鲁棒稳定性提供了凸的充要条件。尤其是，我们证明了结构奇异值始终等于其非负矩阵的凸上限，并且我们使用此结果来得出必要且充分的线性矩阵不等式（LMI）条件，以实现仅涉及系统静态增益的鲁棒稳定性。我们展示了如何将该方法应用于存在不确定干扰的无线网络中用于功率控制的Foschini-Miljanic算法的鲁棒稳定性。

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来源
《IEEE Transactions on Automatic Control》 |2016年第7期|1965-1971|共7页
作者
Marcello Colombino; Roy S. Smith;
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作者单位

Automatic Control Laboratory, Swiss Federal Institute of Technology, Zürich 8092, Switzerland;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Linear matrix inequalities; positive systems; robust stability; structured singular value;

机译：线性矩阵不等式;正系统;鲁棒稳定性;结构奇异值;

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机译：不确定线性正系统通过积分线性约束的鲁棒稳定性和稳定性：L_1-增益和L_∞-增益表征
2. STABILITY OF THE CONVEX LINEAR COMBINATION OF POSITIVE LINEAR SYSTEMS [J] . Tadeusz Kaczorek Asian Journal of Control . 2013,第6期

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3. Stability and robust stability of switched positive linear systems with all modes unstable [J] . Shaoxia Feng, Juan Wang, Jun Zhao Automatica Sinica, IEEE/CAA Journal of . 2019,第1期

机译：具有所有模式不稳定的切换正线性系统的稳定性和鲁棒稳定性
4. Convex characterization of robust stability analysis and control synthesis for positive linear systems [C] . Colombino Marcello, Smith Roy S. IEEE Annual Conference on Decision and Control . 2014

机译：正线性系统鲁棒稳定性分析和控制综合的凸刻画
5. Applications of Fixed Point Theory to Distributed Optimization, Robust Convex Optimization, and Stability of Stochastic Systems [D] . Alaviani, Seyyed Shaho. 2019

机译：固定点理论在分布式优化，鲁棒凸优化和随机系统稳定性的应用
6. Stability criteria on delay-dependent robust stability for uncertain neutral stochastic nonlinear systems with time-delay [O] . Tengyu Ma, Longsuo Li -1

机译：具有时滞的不确定中立随机非线性系统的时滞相关鲁棒稳定性的稳定性判据
7. A Convex Characterization of Robust Stability for Positive and Positively Dominated Linear Systems [O] . Colombino, Marcello, Smith, Roy S. 2015

机译：正和稳态鲁棒稳定性的凸性刻画积极支配的线性系统

A Convex Characterization of Robust Stability for Positive and Positively Dominated Linear Systems

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