In　this　paper,　we　deal　with　stability　analysis　of　a　class　of　nonlinear　switched　discrete-time　systems.　Systems　of　the　class　appear　in　numerical　simulation　of　continuous-time　switched　systems.　Some　linear　matrix　inequality　type　stability　conditions,　based　on　the　common　Lyapunov　function　approach,　are　obtained.　It　is　shown　that　under　these　conditions　the　system　remains　stable　for　any　switching　law.　The　obtained　results　are　applied　to　the　analysis　of　dynamics　of　a　discrete-time　switched　population　model.　Finally,　a　continuous　state　feedback　control　is　proposed　that　guarantees　the　uniform　ultimate　boundedness　of　switched　systems　with　uncertain　nonlinearity　and　parameters.