A heuristic approach to solving a class of bilinear matrix inequality problems

✍ Scribed by Feng Zheng; Qing-Guo Wang; Tong Heng Lee

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 153 KB
• Volume: 47
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(02)00181-0

✦ Synopsis

Many canonical and modern control problems can be recast into the problem of a group of matrix inequalities. Some of them are in the form of linear matrix inequalities (LMIs), which can be solved very e ciently by the powerful LMI toolbox in Matlab, but some others are in the form of bilinear matrix inequalities. The characteristic of this latter class of problems is that when the so called "communicating variables" are ÿxed, the overall problem will be reduced to the problem in LMIs. Thus, how to ÿnd the communicating variables is the key to solve the whole problem. In this paper, an optimal estimate for the communicating variables is presented. We will illustrate our method by completely solving the problems of overshoot bound control and reachable set analysis for uncertain systems. Numerical examples are provided to show the e ectiveness of the proposed method.