Hybrid System Model Transformation And Stability Analysis

Hybrid system contain discrete event and continuous variable and they interaction between the dynamic system. The main theoretical of the hybrid system is to solve research, analysis and synthesis of the modeling theory and method. Switching system is a kind of discrete and continuous dynamic system, it can be seen as a hybrid system consists of several differential equation and the role of switching rules in the form. In recent years, many people pay attention to switch system and in-depth research and gained a lot of achievements, especially in its stability.Based on the previous research, the paper make a further research and exploration. of the theory of hybrid system . The study focused on the main content of the hybrid system model analysis and stability study. For hybrid system, main models of several common model of the internal structure analysis and the mutual conversion. For stability analysis is on research of switching system asymptotically stable. The the paper mainly include the following aspects:1. To discussed the research of the hybrid system on automatic control. From the model, the classification system, control and application were discussed, and points out that the analysis of present hybrid system bottlenecks and existing problems.2. Several common hybrid system model. Mainly introduces several typical models, and analyses its internal structure and mutual conversion probability, and its mutual transformation of the case study.3. A class of continuous type delay switch system stability analysis. Mainly on a class of continuous time-varying delay switch system, through make the proper Lyapunov function structure, using the linear matrix inequality(LMI) method, and discuss the energy of the system, to proof the stability of the system on arbitrary switching.4. One class of discrete switching system is asymptotically stable. The chapter is studied a class of uncertain discrete time-delay with switch control system and make Lyapunov functionals, using the linear matrix inequality(LMI) method system is asymptotically stable results, and the results are verified by the example.5. The stability of continuous and discrete subsystem. Using multiple Lyapunov function, the continuous and discrete system comparison principle gives this kind of switching system stable bilateral degrees of a result, when the continuous and discrete subsystem number is limited, we based on the results to get a more detailed results, through an example to verify its validity.