  We consider the problem of synthesizing optimal linear feedback policies
subject to arbitrary convex constraints on the feedback matrix. This is known
to be a hard problem in the usual formulations ($\Htwo,\Hinf,\LQR$) and
previous works have focused on characterizing classes of structural constraints
that allow efficient solution through convex optimization or dynamic
programming techniques. In this paper, we propose a new control objective and
show that this formulation makes the problem of computing optimal linear
feedback matrices convex under arbitrary convex constraints on the feedback
matrix. This allows us to solve problems in decentralized control (sparsity in
the feedback matrices), control with delays and variable impedance control.
Although the control objective is nonstandard, we present theoretical and
empirical evidence that it agrees well with standard notions of control. We
also present an extension to nonlinear control affine systems. We present
numerical experiments validating our approach.
