Multiobjective state-feedback control design with non-common LMI solutions: change of variables via affine functions

Abstract

This paper presents a new approach with noncommon 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 nonconvex constraints at the sacrifice of conservatism. To get around the conservatism, in this paper, we perform a standard procedure called change of variables and represent the resulting variables as a set of affine functions of new variables. These affine functions are such that they satisfy the nonconvex constraints regardless of the new variables. With these affine functions, we readily derive a set of LMI conditions that allow noncommon LMI solutions.