论文标题
基于Riccati的反馈稳定索引-1描述符系统的插值投影技术
Interpolatory projection technique for Riccati-based feedback stabilization of index-1 descriptor systems
论文作者
论文摘要
这项工作旨在通过基于Riccati的反馈稳定来稳定不稳定的索引1描述符系统，这是一种基于双层式插值技术的修改形式的迭代理性Krylov算法（IRKA）。在基本的IRKA中，对于稳定的系统，可以方便地找到减少的订单模型（ROM），但它不适用于不稳定的模型。在拟议的技术中，最初的反馈是在Irka方法的投影仪的构建中实现的。从Irka获得的ROM估算了Riccati方程的解，因此获得了低级反馈矩阵。使用反向投影过程，对于完整模型，从低级别反馈矩阵中检索了最佳反馈矩阵。最后，为了验证所提出的技术的适当性和能力，它将应用于不稳定的索引-1描述符系统。叙述了本工作与以前的两项作品的比较。模拟是通过使用MATLAB进行数值计算来完成的，并且表格方法和图形方法都用作比较分析的支持工具。
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.
