Robust and minimum norm pole assignment with periodic state feedback
Robust and minimum norm pole assignment with periodic state feedback
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DOI：
10.1109/cdc.1998.761826
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发表时间：
1998-12
期刊：
影响因子：
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通讯作者：
A. Varga
中科院分区：
文献类型：
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作者：
A. Varga
提出了一种求解线性周期离散时间系统最小范数和/或鲁棒极点配置问题的计算方法。所提出的方法使用一个周期性的西尔维斯特方程为基础的参数化的周期极点配置问题，并利用非唯一性的问题，通过施加条件的规范所得到的周期性状态反馈和/或对条件数的周期性特征向量矩阵的闭环系统。求解方法依赖于在适当定义的成本函数上使用梯度搜索方法。给出了代价函数梯度的显式表达式，并讨论了代价函数和梯度的有效计算。数值例子说明了所提出的方法的有效性。
A computational approach is proposed to solve the minimum norm and/or robust pole assignment problem for linear periodic discrete-time systems. The proposed approach uses a periodic Sylvester equation based parametrization of the periodic pole assignment problem and exploits the non-uniqueness of the problem by imposing conditions on the norm of the resulting periodic state feedback and/or on the condition numbers of the periodic eigenvector matrices of the closed-loop system. The solution method relies on using gradient search methods on suitably defined cost functions. Explicit expression of the gradients of cost functions are derived and the efficient evaluation of the cost functions and gradients is discussed. Numerical examples illustrate the effectiveness of the proposed approach.