Controller reduction using structurally balanced truncation method with new closed-loop structures

In this paper, we discuss controller reduction using structurally balanced truncation (SBT) method with new closed-loop structures. The most consequential disadvantage in SBT method is the problem for feasibility of Lyapunov inequalities for closed-loop systems and it still remain open to this date. The new closed-loop structures are introduced in order to relax the feasibility. Finally, a numerical example is used to verify the availability of the proposed methods.