A linear matrix inequality approach to H∞ controller order reduction with stability and performance preservation

H_∞ controller order reduction with stability and performance preservation pose unique challenges to designers. In the paper, an approach for controller order reduction based on minimization of the rank of a matrix variable, subject to linear matrix inequality constraints, is presented. In this approach, the rank of a residue matrix of a high-order controller subject to the error between the loop gain of the closed-loop nominal system and the loop gain of the closed-loop system with the reduced order controller is minimized. However, since solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with the nuclear-norm that can be reduced to a semidefinite program, so that it can be solved efficiently. It is shown that the reduced order controller preserves the performances and stability of the nominal closed-loop system. The proposed approach is applied to an H_∞ high-order controller which is designed for an active suspension system. The performance and stability achieved by the reduced order controller is compared with those achieved by the high-order controller. The comparison is based on experimental results obtained by digital controller implementation.