Positive real control for uncertain two-dimensional systems
Positive real control for uncertain two-dimensional systems
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DOI：
10.1109/tcsi.2002.804531
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发表时间：
2002-12
影响因子：
5.1
通讯作者：
Shengyuan Xu;J. Lam;Zhiping Lin;K. Gałkowski
中科院分区：
文献类型：
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作者：
Shengyuan Xu;J. Lam;Zhiping Lin;K. Gałkowski
本文讨论了由Fornasini-Marchesini局部状态空间模型描述的不确定二维离散系统的正实控制问题。参数不确定性具有时不变性和范数有界性。我们要解决的问题是设计一个状态反馈控制器，使不确定系统鲁棒镇定，并对所有允许的不确定性实现闭环系统的扩展严格正实。建立了2-D离散系统的一种正实形式。在此基础上，以线性矩阵不等式的形式给出了正实控制问题可解的条件。此外，还给出了期望状态反馈控制器的解。最后，给出了一个数值算例来说明该方法的适用性。
This brief deals with the problem of positive real control for uncertain two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini local state-space model. The parameter uncertainty is time-invariant and norm-bounded. The problem we address is the design of a state feedback controller that robustly stabilizes the uncertain system and achieves the extended strictly positive realness of the resulting closed-loop system for all admissible uncertainties. A version of positive realness for 2-D discrete systems is established. Based on this, a condition for the solvability of the positive real control problem is derived in terms of a linear matrix inequality. Furthermore,the solution of a desired state feedback controller is also given. Finally, we provide a numerical example to demonstrate the applicability of the proposed approach.