This paper is concerned with the stability and l₂-gain performance for a class of discrete-time Lur'e systems with an asynchronous controller.A hidden Markov model (HHM) is introduced to describe the asynchronization that appears between the designed controller and the original system.The linear matrix inequality (LMI) approach is utilized to analyze the stability of the closed-loop system and l₂-gain performance.Then a sufficient condition is proposed to guarantee the stochastic stability of the closed-loop system,and to minimize the obtained l₂-gain from the disturbance to output.Thus,an asynchronous controller consisting of both linear state feedback and cone-bounded nonlinear output feedback can be designed by solving the given conditions.A simulation example is given to demonstrate the effectiveness of the proposed method.