This paper presents an overview of a linear matrix inequality (LMI) approach to the multiobjective synthesis of linear output-feedback controllers, The design objectives can be a mix of H-infinity performance, H-2 performance, passivity, asymptotic disturbance rejection, time-domain constraints, and constraints on the closed-loop pole location, In addition, these objectives can be specified on different channels of the closed-loop system, When all objectives are formulated in terms of a common Lyapunov function, controller design amounts to solving a system of linear matrix : inequalities, The validity of this approach is illustrated by a realistic design example.