  Operator splitting methods solve composite optimization problems by breaking
them into smaller sub-problems that can be solved sequentially or in parallel.
In this paper, we propose a unified framework for certifying both linear and
sublinear convergence rates for three-operator splitting (TOS) method under a
variety of assumptions about the objective function. By viewing the algorithm
as a dynamical system with feedback uncertainty (the oracle model), we leverage
robust control theory to analyze the worst-case performance of the algorithm
using matrix inequalities. We then show how these matrix inequalities can be
used to verify sublinear/linear convergence of the TOS algorithm and guide the
search for selecting the parameters of the algorithm (both symbolically and
numerically) for optimal worst-case performance. We illustrate our results
numerically by solving an input-constrained optimal control problem.
