A cone programming approach to the bilinear matrix inequality problem and its geometry |
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| Authors: | Mehran Mesbahi George P Papavassilopoulos |
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| Institution: | (1) Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, 91109 Pasadena, CA, USA;(2) Department of Electrical Engineering - Systems, University of Southern California, 90089-2563 Los Angeles, CA, USA |
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| Abstract: | We discuss an approach for solving the Bilinear Matrix Inequality (BMI) based on its connections with certain problems defined
over matrix cones. These problems are, among others, the cone generalization of the linear programming (LP) and the linear
complementarity problem (LCP) (referred to as the Cone-LP and the Cone-LCP, respectively). Specifically, we show that solving
a given BMI is equivalent to examining the solution set of a suitably constructed Cone-LP or Cone-LCP. This approach facilitates
our understanding of the geometry of the BMI and opens up new avenues for the development of the computational procedures
for its solution.
Research supported in part by the National Science Foundation under Grant CCR-9222734. |
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| Keywords: | Bilinear matrix inequalities Linear complementarity problem over cones Linear programming over cones Robust control |
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