A Spectral Quadratic-SDP Method with Applications to Fixed-Order H2 and H∞ Synthesis

In this paper, we discuss a spectral quadratic-SDP method for the iterative resolution of fixed-order H2 and H∞ design problems. These problems can be cast as regular SDP programs with additional nonlinear equality constraints. When the inequalities are absorbed into a Lagrangian function the problem reduces to solving a sequence of SDPs with quadratic objective function for which a spectral SDP method has been developed. Along with a description of the spectral SDP method used to solve the tangent subproblems, we report a number of computational results to validate our approach.