Robust stability and stabilization for singular systems with state delay and parameter uncertainty
Robust stability and stabilization for singular systems with state delay and parameter uncertainty
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DOI：
10.1109/tac.2002.800651
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发表时间：
2002-08
期刊：
影响因子：
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通讯作者：
Shengyuan Xu;P. Dooren;R. Ştefan;J. Lam
中科院分区：
文献类型：
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作者：
Shengyuan Xu;P. Dooren;R. Ştefan;J. Lam
研究了具有状态时滞的不确定连续广义系统的鲁棒稳定性和镇定问题。假设参数不确定性是范数有界的。鲁棒稳定性问题的目的是给出不确定广义系统对于所有允许的不确定性都是正则的、无脉冲的和稳定的条件，而鲁棒镇定的目的是设计一个状态反馈控制律，使得所得到的闭环系统是鲁棒稳定的。这些问题分别通过广义二次稳定和广义二次稳定的概念得到解决。给出了广义二次稳定和广义二次镇定的充要条件。提出了一种严格线性矩阵不等式(LMI)设计方法。给出了所需的鲁棒状态反馈控制律的显式表达式。最后，给出了一个数值算例，说明了该方法的应用。
Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method.