A Mesh-Based Partitioning Algorithm for Decreasing Conservatism in Solving BMI Problems

A Mesh-Based Partitioning Algorithm to solve Bilinear Matrix Inequality problems (BMIs) is proposed in the following paper. - H. Javanmardi, M. Dehghani, M. Mohammadi, and M.R. Hesamzadeh, "A Mesh-Based Partitioning Algorithm for Decreasing Conservatism in Solving BMI Problems", Accepted to be published at Optimal Control Applications and methods. The main idea is to divide the solution space of a non-convex BMI problem into smaller parts in the form of simplexes through meshing the space. In each simplex, only the concave part of BMI constraints is approximated by piecewise affine matrix, which eventually leads to a convex sub-problem. After that, the feasible solution can be easily obtained in each simplex through the Linear Matrix Inequality (LMI) optimization. The detailed results of solving output feedback controller design problem in the form of BMI exploiting the novel mesh method is attached.