This paper investigates the problem of resource allocation for a wireless communication network with distributed reconfigurable intelligent surfaces (RISs). In this network, multiple RISs are spatially distributed to serve wireless users and the energy efficiency of the network is maximized by dynamically controlling the on-off status of each RIS as well as optimizing the reflection coefficient matrix of the RISs. This problem is posed as a joint optimization problem of transmit power and RIS control, whose goal is to maximize the energy efficiency under minimum rate constraints of the users. To solve this problem, an alternating algorithm is proposed by solving two sub-problems iteratively. The phase optimization sub-problem is solved by using a successive convex approximation method, which admits a closed-form solution at each step. Moreover, the RIS on-off optimization sub-problem is solved by using the dual method. Simulation results show that the proposed scheme achieves up to 27% and 68% gains in terms of the energy efficiency compared to the conventional RIS scheme and amplify-and-forward relay scheme, respectively.