Output Feedback Controller Design for Discrete LTI Systems with Polytopic Uncertainty

This paper concerns static output feedback stabilization of polytopic discrete LTI systems. The previous related studies were mainly based on LMI approaches which are naturally conservative. In this paper, a novel design algorithm is presented that iteratively partitions a primary design space to subspaces. Then, by assessing stabilizability status of each generated subspace, the algorithm determines the total stabilizable parts and removes the undesired parts of the design space. Mathematical theories are developed to predict the total De-stabilizability or stabilizability of a given subspace. These subspaces’ properties are detected through checking the existence of critical polynomials (which have roots on the unit circle of the complex plane) on their exposed edges. By omitting the undesired parts of the design space, the algorithm just searches the desired parts which are far smaller than the primary design space. This strategy improves the feasibility performance of the algorithm. Some illustrating examples are provided to show the steps and iterations of the design algorithm. Furthermore, one hundred random models are generated to evaluate the feasibility performance of the proposed algorithm as compared to some existing methods. The results reveal the superiority of the proposed algorithm.

本研究论文聚焦于多边形离散线性时不变（LTI）系统的静态输出反馈稳定化问题。先前相关研究主要基于线性矩阵不等式（LMI）方法，该方法本质上较为保守。本文提出了一种新颖的设计算法，该算法通过迭代划分基本设计空间为子空间。随后，通过评估每个生成的子空间的稳定性，算法确定总的可稳定部分，并移除设计空间中的不期望部分。针对给定子空间的总体去稳定化或稳定化，发展了数学理论进行预测。通过检查临界多项式（其根位于复平面的单位圆上）在子空间的暴露边缘的存在性，检测这些子空间的属性。通过移除设计空间中的不期望部分，算法仅搜索远小于基本设计空间的需求部分。此策略提升了算法的可行性性能。提供了一些示例来说明设计算法的步骤和迭代过程。此外，生成了100个随机模型以评估所提算法的可行性性能，并与一些现有方法进行比较。结果显示，所提算法具有优越性。