A successive convex optimization method for bilinear matrix inequality problems and its application to static output‐feedback control.

This article explores a successive convex optimization method for solving a class of nonconvex programming problems subject to bilinear matrix inequality (BMI) constraints. In particular, many control issues can be boiled down to BMI problems, which are typically NP‐hard. To get out of the predicament, we propose a more relaxed feasible set to approximate the original one, based on which a local optimization algorithm is developed and its convergence is analyzed. As a case of application, we consider static output‐feedback control for uncertain systems with disturbances in restricted frequency intervals. In order to strengthen the disturbance‐rejection capability over the given frequency range, we establish sufficient and necessary analysis conditions via the generalized Kalman‐Yakubovich‐Popov lemma, under which the homogeneous polynomially parameter‐dependent technique is adopted to facilitate the design. Finally, several examples are given to demonstrate the efficiency of the results. [ABSTRACT FROM AUTHOR]