This paper tackles the problem of robust $$$ {H}_{\infty } $$$ memory observer design problem for discrete-time switched nonlinear systems by using past output measurements. Different from traditional design strategies of Luenberger-type observers using the current output measurements, the memory Luenberger-type observer design strategy introduces the past output measurements of switched systems and observers simultaneously. In addition, in order to better describe the observer error systems, a novel augmented state variable framework of the observer error systems is developed. The highlight of this paper lies that the memory observer design strategy is developed by considering past output measurements and state error values of memory observers, whose performance can be improved by increasing the number of past output measurements used in the observer design, which is an important discovery and significant novelty of this work. By combining the multiple Lyapunov functions approach and average dwell time technique, and introducing matrix variables with free structure, new sufficient conditions for weighted $$$ {H}_{\infty } $$$ performance analysis of observer error systems are derived. Then, the memory observer synthesis conditions are obtained in the form of linear matrix inequality (LMI), and the memory observers can be obtained by solving these LMIs. Lastly, two examples are presented to show the advantages and effectiveness of the derived results.