指数-1广义系统Riccati反馈镇定的插值投影方法
Interpolatory projection technique for Riccati-based feedback stabilization of index-1 descriptor systems
摘要：
针对一类不稳定指数为1的广义系统，提出了一种改进的基于双切插值的迭代有理Krylov算法（IRKA），并利用Riccati反馈镇定方法进行镇定.在基本的IRKA中，对于稳定的系统，可以方便地找到降阶模型（ROM），但它不适用于不稳定的系统。在所提出的技术中，在IRKA方法的投影仪的构造内实现初始反馈。由IRKA得到的ROM估计Riccati方程的解，从而得到低秩反馈矩阵。使用反向投影过程，对于完整模型，从低秩反馈矩阵中检索最优反馈矩阵。最后，为了验证所提出的技术的适用性和能力，它被应用到不稳定指数-1广义系统。叙述了目前的工作与以前的两个作品的比较。利用MATLAB进行了数值计算，并以表格法和图解法作为对比分析的辅助工具。
英文摘要：
The work aims to stabilize the unstable index-1 descriptor systems by Riccati-based feedback stabilization via a modified form of Iterative Rational Krylov Algorithm (IRKA), which is a bi-tangential interpolation-based technique. In the basic IRKA, for the stable systems the Reduced Order Models (ROMs) can be found conveniently, but it is unsuitable for the unstable ones. In the proposed technique, the initial feedback is implemented within the construction of the projectors of the IRKA approach. The solution of the Riccati equation is estimated from the ROM achieved by IRKA and hence the low-rank feedback matrix is attained. Using the reverse projecting process, for the full model the optimal feedback matrix is retrieved from the low-rank feedback matrix. Finally, to validate the aptness and competency of the proposed technique it is applied to unstable index-1 descriptor systems. The comparison of the present work with two previous works is narrated. The simulation is done by numerical computation using MATLAB, and both the tabular method and graphical method are used as the supporting tools of comparative analysis.
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