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Title: A heuristic approach to solving a class of bilinear matrix inequality problems
Authors: Zheng, F. 
Wang, Q.-G. 
Lee, T.H. 
Keywords: Bilinear matrix inequalities
Overshoot bound control
Reachable set analysis
Issue Date: 7-Oct-2002
Citation: Zheng, F., Wang, Q.-G., Lee, T.H. (2002-10-07). A heuristic approach to solving a class of bilinear matrix inequality problems. Systems and Control Letters 47 (2) : 111-119. ScholarBank@NUS Repository.
Abstract: 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 efficiently 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 fixed, the overall problem will be reduced to the problem in LMIs. Thus, how to find 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 effectiveness of the proposed method. © 2002 Elsevier Science B.V. All rights reserved.
Source Title: Systems and Control Letters
ISSN: 01676911
DOI: 10.1016/S0167-6911(02)00181-0
Appears in Collections:Staff Publications

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