  In this work, we consider non-collocated sensors and actuators, and we
address the problem of minimizing the number of sensor-to-actuator
transmissions while ensuring that the L2 gain of the system remains under a
threshold. By using causal factorization and system level synthesis, we
reformulate this problem as a rank minimization problem over a convex set. When
heuristics like nuclear norm minimization are used for rank minimization, the
resulting matrix is only numerically low rank and must be truncated, which can
lead to an infeasible solution. To address this issue, we introduce approximate
causal factorization to control the factorization error and provide a bound on
the degradation of the L2 gain in terms of the factorization error. The
effectiveness of our method is demonstrated using a benchmark.
