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.