Nonconvex spectral algorithm for solving BMI on the reduced order H∞ control

The design of reduced-order H∞ control can be transformed into an optimization problem with bilinear matrix inequality (BMI) constraints, which is an NP-hard problem. We propose a method to equivalently transfer the BMI constraint into a convex LMI constraint plus a matrix-rank constraint. The optimization with matrix-rank constraint is iteratively solved by a sequence of semidefinite programming (SDP) problems. Simulations on several benchmark systems show that our algorithm is practical and efficient.