  We address the problem of sparsity-promoting optimal control of
cyber-physical systems with feedback delays. The delays are categorized into
two classes - namely, intra-layer delay, and inter-layer delay between the
cyber and the physical layers. Our objective is to minimize the H2-norm of the
closed-loop system by designing an optimal combination of these two delays
along with a sparse state-feedback controller, while respecting a given
bandwidth constraint. We propose a two-loop optimization algorithm for this.
The inner loop, based on alternating directions method of multipliers (ADMM),
handles the conflicting directions of decreasing H2-norm and increasing
sparsity of the controller. The outer loop comprises of semidefinite program
(SDP)-based relaxations of non-convex inequalities necessary for stable
co-design of the delays with the controller. We illustrate this algorithm using
simulations that highlight various aspects of how delays and sparsity impact
the stability and $\mc{H}_2$ performance of a LTI system.
