The main aim of this thesis is to design a methodology for modeling, analysis and control of hybrid systems in the context of cyber-physical systems and their subsequent implementation into the distributed control system. The thesis deals with selected methods and algorithms for modeling and control of hybrid systems, which were modified to the conditions of the Center of Modern Control Techniques and Industrial Informatics at KKUI FEEI TU and to the tasks within the experiment at ALICE CERN. These methods and algorithms are then validated both on simulation and laboratory model applications. The thesis contains a comprehensive methodology for modeling of hybrid systems, both for discrete-state systems with defined continuous dynamics in each state and for systems with discrete states without defined continuous dynamics. Subsequently, in the analysis of hybrid systems, analysis in open-loop as well as phase portraits are used. After the analysis of hybrid systems, control algorithms for selected hybrid systems are designed, whether in the form of optimal control with the application of metaheuristic algorithms or explicit model predictive control. The next part of the thesis deals with the design of adaptive supervisory control using RBF neural networks for the under-actuated inverted pendulum system with a linear synchronous motor. The methodology and its subsequent verification are elaborated within the thesis in four case studies and two research tasks of the experiment at ALICE CERN. The software output of the thesis is implemented in MATLAB/Simulink using application toolboxes, in C++ language and in WinCC OA.