  This paper focuses on the design of time-invariant memoryless control
policies for fully observed controlled Markov chains, with a finite state
space. Safety constraints are imposed through a pre-selected set of forbidden
states. A state is qualified as safe if it is not a forbidden state and the
probability of it transitioning to a forbidden state is zero. The main
objective is to obtain control policies whose closed loop generates the maximal
set of safe recurrent states, which may include multiple recurrent classes. A
design method is proposed that relies on a finitely parametrized convex program
inspired on entropy maximization principles. A numerical example is provided
and the adoption of additional constraints is discussed.
