Abstract
This paper presents a new approach with non-common linear matrix inequality (LMI) solutions to the multiobjective state-feedback control design problem. A conventional approach is adopting common LMI solutions to avoid a difficulty of non-convex constraints at the sacrifice of conservatism. To reduce the conservatism, in this paper, we introduce some additional constraints to variables so that we convexify the problem and obtain LMI conditions that leave the feedback gain directly as one of the variables. Because of the freedom in the variables satisfying the constraints, our approach turns out to give a set of LMI conditions that allow non-common LMI solutions. Furthermore, an effective iterative algorithm follows immediately from the present approach, with which we can reduce the conservatism considerably.
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