A simple numerical method for minimizing the maximum eigenvalues of symmetric matrices via nonlinear differential equation solvers (Towards H_∞ control design based on bilinear matrix inequalities)

摘要

We present a simple numerical method for minimizing the maximum eigenvalues of real-valued symmetric matrices, based on nonlinear differential equation solvers. First, we convert the minimiza- tion problem for the maximum eigenvalues, which is nondifferentiale, into a differentiable optimiza- tion problem by means of interior point methods. Second, making use of differential equation solvers, we present a simple method for solving the optimization problem.