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

Feng Zheng, Qing Guo Wang, Tong Heng Lee

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)111-119
Number of pages9
JournalSystems and Control Letters
Issue number2
Publication statusPublished - 7 Oct 2002
Externally publishedYes


  • Bilinear matrix inequalities
  • Overshoot bound control
  • Reachable set analysis

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


Dive into the research topics of 'A heuristic approach to solving a class of bilinear matrix inequality problems'. Together they form a unique fingerprint.

Cite this