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 include $ H_{\infty} $ performance, $ H_{2} $ performance, passivity, asymptotic disturbance rejection, time-domain constraints, and constraints on the closed-loop pole location. 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 reduces to solving a system of linear matrix inequalities. The validity of this approach is illustrated by a realistic design example. The paper discusses various specifications and objectives that can be formulated in terms of LMI's, including $ H_{\infty} $ performance, general quadratic constraints, $ H_{2} $ performance, peak impulse response and settling time, peak-to-peak gain, regional pole constraints, nominal regulation, and robust regulation. The LMI approach allows for the systematic transformation of these specifications into LMI constraints, enabling the design of controllers that meet multiple objectives simultaneously. The key idea is to use a change of controller variables to linearize the problem and convert it into a set of LMI's. This approach allows for the use of efficient interior-point algorithms to solve the optimization problem. The paper also discusses the implications of using a single Lyapunov function for all specifications, which can introduce conservatism but allows for a more systematic and efficient design process. The paper concludes with a detailed discussion of the LMI approach to multiobjective synthesis, emphasizing its numerical tractability, ability to handle multiple objectives, and the flexibility it provides in shaping the Lyapunov matrix to meet various performance requirements. The approach is shown to be more effective than classical synthesis techniques, particularly in handling complex designs with multiple specifications.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 include $ H_{\infty} $ performance, $ H_{2} $ performance, passivity, asymptotic disturbance rejection, time-domain constraints, and constraints on the closed-loop pole location. 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 reduces to solving a system of linear matrix inequalities. The validity of this approach is illustrated by a realistic design example. The paper discusses various specifications and objectives that can be formulated in terms of LMI's, including $ H_{\infty} $ performance, general quadratic constraints, $ H_{2} $ performance, peak impulse response and settling time, peak-to-peak gain, regional pole constraints, nominal regulation, and robust regulation. The LMI approach allows for the systematic transformation of these specifications into LMI constraints, enabling the design of controllers that meet multiple objectives simultaneously. The key idea is to use a change of controller variables to linearize the problem and convert it into a set of LMI's. This approach allows for the use of efficient interior-point algorithms to solve the optimization problem. The paper also discusses the implications of using a single Lyapunov function for all specifications, which can introduce conservatism but allows for a more systematic and efficient design process. The paper concludes with a detailed discussion of the LMI approach to multiobjective synthesis, emphasizing its numerical tractability, ability to handle multiple objectives, and the flexibility it provides in shaping the Lyapunov matrix to meet various performance requirements. The approach is shown to be more effective than classical synthesis techniques, particularly in handling complex designs with multiple specifications.