  This paper introduces a decentralized state-dependent Markov chain synthesis
(DSMC) algorithm for finite-state Markov chains. We present a state-dependent
consensus protocol that achieves exponential convergence under mild technical
conditions, without relying on any connectivity assumptions regarding the
dynamic network topology. Utilizing the proposed consensus protocol, we develop
the DSMC algorithm, updating the Markov matrix based on the current state while
ensuring the convergence conditions of the consensus protocol. This result
establishes the desired steady-state distribution for the resulting Markov
chain, ensuring exponential convergence from all initial distributions while
adhering to transition constraints and minimizing state transitions. The DSMC's
performance is demonstrated through a probabilistic swarm guidance example,
which interprets the spatial distribution of a swarm comprising a large number
of mobile agents as a probability distribution and utilizes the Markov chain to
compute transition probabilities between states. Simulation results demonstrate
faster convergence for the DSMC based algorithm when compared to the previous
Markov chain based swarm guidance algorithms.
