This paper formulates and solves the robust H∞ control problem for discrete-time nonlinear switching systems. The H∞ control problem is interpreted as the l2 finite gain control problem and is studied using a dissipative systems theory for switched systems. Both state and measurement feedback control problems are formulated as dynamic games and solved using dynamic programming. The partially observed dynamic game corresponding to the measurement feedback control problem is solved by transforming into a completely observed, full state infinite-dimensional game problem using information states. Our results are illustrated with an example. Copyright © 2007 John Wiley & Sons, Ltd.