Abstract
In this paper, we present a simple numerical method for solutions of linear/bilinear matrix inequalities (LMI/BMI) problems, more exactly a method for minimizing the maximum eigenvalues of real valued symmetric matrices. Nonlinear differential equation solvers are used in our approach. First, we convert the non-differentiable minimization problem for the maximum eigenvalues into one of differentiable optimization problems by means of interior point methods. Second, making use of differential equation solvers, we present a simple method for finding the solutions of the optimization problems. Finally, we demonstrate the effectiveness of the algorithm through some simulation experiences.
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