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Robust stability and stabilization of discrete singular systems: an equivalent characterization

机译：离散奇异系统的鲁棒稳定性和稳定性：等效表征

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摘要

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.
机译：本文讨论了不确定的离散时间奇异系统的鲁棒稳定性和稳定性问题。假设参数不确定性是时不变的，并且在状态矩阵和输入矩阵中均出现范数界。根据严格的线性矩阵不等式（LMI），提出了离散时间奇异系统是规则，因果和稳定的新的充要条件。在此基础上，引入了不确定离散广义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，获得了广义二次稳定性和广义二次稳定的充要条件。在这些条件下，解决了鲁棒稳定性和鲁棒稳定性的问题。还给出了所需状态反馈控制器的明确表达式，该表达式不涉及矩阵分解。最后，提供了一个说明性示例来证明所提出方法的适用性。

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