Controller reduction with ℋ_∞ error performance: Continuous- and discrete-time cases

This paper is concerned with the problem of ℋ_∞ controller reduction for linear systems. Both continuous- and discrete-time cases are considered, with necessary and sufficient conditions obtained for the existence of desired reduced order controllers. In solving this problem, two approaches are presented. The first approach is based on the projection lemma, where the admissible controllers can be parameterized after a set of conditions are satisfied; and the second one directly incorporates the controller matrices to be determined into a set of conditions by introducing new techniques, and thus no parameterization procedure is needed. These necessary and sufficient conditions are formulated in terms of linear matrix inequalities (LMIs) plus some equality constraints. Since these conditions are not convex, the cone complementarity linearization (CCL) idea is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be readily solved by standard numerical software. A numerical example shows the effectiveness of the controller reduction methods.