Robust stability and stabilization of discrete singular systems: an equivalent characterization
Robust stability and stabilization of discrete singular systems: an equivalent characterization
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DOI：
10.1109/tac.2003.822854
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发表时间：
2004-04
影响因子：
6.8
通讯作者：
Shengyuan Xu;J. Lam
中科院分区：
文献类型：
--
作者：
Shengyuan Xu;J. Lam
本说明涉及不确定离散时间奇异系统的稳定稳定性和稳定问题的问题。假定参数不确定性是在状态和输入矩阵中出现的时间不变和范围内的。根据严格的线性矩阵不等式（LMI），提出了一个新的必要条件，使离散时间单数系统是规则，因果和稳定的。基于此，引入了不确定的离散时间单数系统的广义二次稳定性和广义二次稳定的概念。分别根据严格的LMI和一组矩阵不等式获得了通用二次稳定性和广义二次稳定的必要条件。在这些条件下，解决了稳健稳定性和稳定稳定的问题。还给出了所需状态反馈控制器的明确表达，其中涉及矩阵分解。最后，提供了一个说明性的示例，以证明所提出的方法的适用性。
This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.