An LMI approach to gain parameter design for regional eigenvalue/eigenstructure assignment

In this paper, an LMI (linear matrix inequality) method to design feedback gain parameters for regional eigenvalue/eigenstructure assignment is proposed. The problem setting of regional eigenvalue/eigenstructure assignment is totally different from eigenvalue clustering (i.e. root clustering or D-stabilization) and design problem of state feedback gain parameters was formulated as an LMI problem with nonconvex rank-one constraint in the authors' previous work. The main contribution of this paper is to prove that the above rank-one constraint is irrelevant when each assignment set is convex. Numerical examples are shown to illustrate the proposed method