  Given a Markov decision process (MDP) and a linear-time ($\omega$-regular or
LTL) specification, the controller synthesis problem aims to compute the
optimal policy that satisfies the specification. More recently, problems that
reason over the asymptotic behavior of systems have been proposed through the
lens of steady-state planning. This entails finding a control policy for an MDP
such that the Markov chain induced by the solution policy satisfies a given set
of constraints on its steady-state distribution. This paper studies a
generalization of the controller synthesis problem for a linear-time
specification under steady-state constraints on the asymptotic behavior. We
present an algorithm to find a deterministic policy satisfying $\omega$-regular
and steady-state constraints by characterizing the solutions as an integer
linear program, and experimentally evaluate our approach.
