As the core model of discrete control systems and security verification, the order structure of automata on their state sets plays a key role in network security protocols, quantum secure communication, privacy protection, cryptography, dynamic obstacle avoidance control and other scenarios. Based on this, we study a class of automata with special order structures —monotonic automata (automata whose state set admits a compatible total order) are the extreme case of partially ordered automata. If an automaton A is a monotonic automaton, then its state set forms a forest under the action of any input symbol. We define the structural total order of such forests and prove that A is monotonic if and only if all forests of A corresponding to the input symbols have a common structural total order. Accordingly, a decision algorithm of monotonic automata with time complexity \(O(mn^3)\) is designed.