This paper is concerned with distributed model predictive control for a discrete-time target linear system over a controller communication network with switching topology. The global system is decomposed into N subsystems and N optimization problems are solved in parallel to minimize an upper bound on a robust performance objective by using a state-feedback controller for each subsystem. The considered topology evolution of the control network is assumed to be subject to a Markov chain. An extended cone complementarity linearization method (CCLM) is used to solve the constrained linear matrix inequality (CLMI) and a Bisection method based iterative algorithm is adopted to find the optimal solution. Simulation results illustrate the effectiveness of the proposed method.