Fixed-order control design for LMI control problems using alternating projection methods

This paper suggests some simple computational techniques for control design, for problems described by linear matrix inequalities (LMIs). In particular, we concentrate on the stabilization and the suboptimal H_∞ output-feedback control design problems. These problems can be described by a pair of LMIs and an additional coupling condition. This coupling condition is convex for the full-order control design problem, however convexity is lost for the controller design problem of order strictly less that the plant order. We formulate these problems as feasibility problems with matrix set constraints of simple geometry, and we develop analytical expressions for the projection operators onto these sets. For the full-order design problem, our alternating projection techniques are guaranteed to converge globally to a feasible solution. However, for the low-order case, the convergence is guaranteed only locally. Examples illustrate the suggested approach