This paper deals with one of the challenges of cyber-physical systems, namely modelling them as hybrid systems. Specifically the paper aims to utilize hybrid systems framework onto the lift system which comes from the real laboratory lift. The mathematical model was derived using hybrid automata framework in synergy with linear temporal logic. Hybrid automata framework was used to describe continuous dynamics as well as discrete dynamics of the lift system mathematical model. Linear temporal logic was used to formally define rules according to which the lift system is constrained. The whole logic, system dynamics and constrains are then implemented within MATLAB/Simulink environment using Stateflow toolbox. Finally, the verification of the lift mathematical model is performed within chosen scenarios.