This paper is concerned with the exponential stabilization problem for multi-links complex networks with Markovian switching topologies (MCNMSTs). It is worth emphasizing that the topological structure of multi-links complex networks is Markovian switching and each switching subnetwork is not required to contain a directed spanning tree or to be strongly connected. Moreover, a new type of periodically intermittent discrete-time state observations control (PIDSOC), which means the control is feedback control based on discrete-time state observations during the control time in a control period, is first proposed for the stabilization purpose. By using Lyapunov method and graph theory, some sufficient conditions are established to ensure the exponential stabilization of MCNMSTs. Meanwhile, some corollaries are shown when PIDSOC becomes feedback control based on discrete-time state observations. In addition, our theoretical results are used to discuss exponential stabilization of stochastic coupled oscillators and a sufficient criterion is derived. Finally, a numerical example is given to verify the applicability and effectiveness of the obtained theoretical results.