The paper deals with the developing of the methodological backgrounds for the construction and study of nonlinear dynamical models. Such backgrounds allow us to use interval methods to define piece-wise linear models for the one class chaotic systems. Usage of proposed models is the way to find conditions of chaos occurring in dynamical systems. We prove our approach by considering the example of modeling, simulating, and studying of Mackey-Glass system. This example shows that one can use linear control theory methods to study the dynamic of time-delayed chaotic systems.