This paper addresses a novel incentive and control mechanism among a principal and multiple agents with long-term average reward in stochastically dynamical systems. In actual physical systems such as dynamic power systems, the principal called a system operator cannot directly operate the agents' control input in real time to guarantee the agents' voluntary decision makings. Meanwhile, the operations maximizing the agents' own profit is not always to achieve the social welfare maximization, which is the principal's objective. To avoid such moral hazard, adopting a contract theory approach, we first propose a dynamic incentive and control synthesis problem, where each agent and the principal maximize their own long-term average reward, respectively. We next derive an optimal contract condition and stability condition analytically. Finally, the performance of the proposed contract mechanism is numerically verified through simulations with a four area power network model.