Bilinear Matrix Inequalities in Systems and Control Theory and Algorithms

双线性矩阵不等式（BMI）为鲁棒控制中出现的一类问题提供了一个强有力的公式，例如：定阶h∞、mu / km合成、去中心化、同时稳定等。BMI可以被重新表述为一个非凸规划问题，并且与线性互补问题和半定规划问题有着非常深刻的联系。在最近的出版物中，研究了BMI与这些问题有关的几个方面。提出的研究的基本目的是进一步研究BMI的理论结构，以及开发有效的算法来解决它。开发求解BMI的有效算法将是当前工作的主要部分。我们所追求的理论见解将主要用于获得用于开发此类算法的见解。所采用的方法将依赖于非凸规划的线性互补、半定规划和并行算法领域。与鲁棒控制相关的控制理论的几个实际应用将受益于这样的研究。除了鲁棒控制之外，还有其他领域的应用，如信号和图像处理、经济学、图和组合理论等，这些研究将会用到。＊＊＊

ECS-9729132PapavassilopoulosThe Bilinear Matrix Inequality (BMI) provides a powerful formulation of a large class of problems appearing in robust control, such as: fixed order H-infinity, mu / km synthesis, decentralization, simultaneous stabilization, etc. The BMI can be reformulated as a nonconvex programming problem and has also very deep interconnections with the Linear Complementarity Problem and the Semidefinite Programming Problem. In recent publications several aspects of the BMI pertaining to these problems have been studied. The basic aim of the proposed research is to examine further the theoretical structures of the BMI as well as to develop efficient algorithms for solving it. The development of efficient algorithms for solving BMI's will constitute a major part of the present effort. The theoretical insights that will also be pursued will be primarily utilized for gaining insights to be used in the development of such algorithms. The method to be employed will rely on the areas of Linear Complementarity, Semidefinite Programming and Parallel Algorithms for nonconvex programming. Several practical applications of Control Theory pertaining to robust control stand to benefit from such a study. Besides robust control, there are also other areas of applications such as signal and image processing, economics, graphs and combinatorial theory, etc., where such study will be of use. ***