Local passivity andH∞control of switched discrete-time nonlinear systems are studied using the linearisation technique in this paper. We first establish LMI-based sufficient conditions under which theconsidered system is locally strictly QSR-dissipative. Then, two special cases of QSR-dissipativity, local passivity andl2gain, are investigated. In view of the derived conditions being all convex in linearised system matrices, local feedback passification andH∞control problems of switched discrete-time nonlinear systems are solved. The efficiency of the proposed method is verified through numerical examples. [ABSTRACT FROM PUBLISHER]