An algorithm for solving optimization problems involving special frequency dependent LMIs

The problem of optimizing a linear objective over a set of frequency dependent Linear Matrix Inequalities (LMIs) can frequently be found in systems and control applications. Typically, these problems are solved by transforming the frequency dependent LMIs to non-frequency dependent ones, which are then treated under the framework of semidefinite programming. The transformation, however, requires additional decision variables which increase the computational complexity and reduce the computation speed. In this paper, an alternative solution is proposed. The main feature of the proposed approach is that no additional decision variables are introduced.