This article deals with a novel 2-speed transmission system specifically designed for electric axle applications. The design of this transmission permits seamless gearshifts and is characterized by a simple mechanical layout. The equations governing the overall system dynamics are presented in the paper. The principles of the control system for the seamless gearshifts achievable by the novel transmission prototype - currently under experimental testing at the University of Surrey and on a prototype vehicle - are analytically demonstrated and detailed through advanced simulation tools. The simulation results and sensitivity analyses for the main parameters affecting the overall system dynamics are presented and discussed.