LOW-ORDER CONTROL DESIGN FOR LMI PROBLEMS USING ALTERNATING PROJECTION METHODS

Computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalit ies (LMIs). In particular, we concentrate on the stabilization and the suboptimal H-proportional to output feedback control design problems. These problems can be described by a pair of LMIs and an additional c oupling condition. This coupling condition is convex for the full-orde r control design problem, but convexity is lost for the control proble m of order strictly less than the plant order. Wt: formulate these pro blems as feasibility problems with matrix constraint sets of simple ge ometry, and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets. Full-order an d low-order controllers are designed using alternating projection meth ods. For the full-order controller case, global convergence of the alt ernating projection methods to a feasible solution is guaranteed. Howe ver, for the Low-order control case, only local convergence is guarant eed. An example is provided to illustrate the use of these methods for the full-order and the low-order controller design. Copyright (C) 199 6 Elsevier Science Ltd.