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 1 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.Index Terms-Controller parameter change, linear matrix inequalities, Lyapunov shaping paradigm, multichannel multiobjective control.

This paper describes a new MATLAB-based toolbox for control design via linear matrix inequality (LMI) tecliniques. After a brief review of LMIs and of some 01 their applications to control, the toolbox contents and capabilities are presented.

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