Convex initialization of the H2-optimal static output feedback problem

Recently we have established a link between invariants for quadratic optimization problems and linear-quadratic (LQ) optimal control. The link is that for LQ control one invariant is c_k = u_k - Kx_k, which yields zero loss from optimality when controlled to a constant setpoint c = c_s = 0. In general there exists infinitely many such invariants to a quadratic programming (QP) problem. We show how the link can be used to generate output feedback control by using current and old measurements. In this paper we extend this approach by considering in more detail some interesting examples, and the use of additional (old) measurements. In particular, we show that if the number of measurements is less than the number of disturbances (initial states) plus independent inputs, we can not with this method find a policy u_k = -K^yy_k that minimizes the original problem, because K^y is not optimally constant. However, this method may be used to find initial values for H₂-optimal static output feedback synthesis.