Research On Stability Of Hybrid System And Its Applications In Power Systems

Hybrid systems consist of continuous time and/or discrete time dynamic systems and discrete event systems, which interact on each other. There has been an intensified interest among control engineers in discrete event and hybrid systems during the last decade. For the complex dynamic and particularity of hybrid system, even though the linear hybrid system has very complex nonlinear character. Stability is one of the central properties in system theory and engineering. Many practical systems are hybrid naturally. So it is import for the theory and application to research on the stability and control method of hybrid system.Based on the Lyapunov stability theory of hybrid systems and using Linear Matrix Inequality (LMI) method, this dissertation investigates the stability of hybrid system with uncertain time-varying time-delay perturbation. And the further research is carried out for stability of differential algebraic hybrid system. And the stability theory put forward in the dissertation is used in the analysis and control of voltage stability of power system.The research of hybrid system is overviewed form the view of automatically control. Based on the analysis of hybrid system model in existence, it is pointed out that stability of hybrid system is the research emphasis on the stage. Many significant results are derived from Lyapunov direct method. Further more, it is discussed in detail for the application of hybrid system in power system.Using Single Lyapunov function and Multiple Lyapunov function, the switching laws are designed to analyze the stability of the whole hybrid system with uncertain time-varying time-delay perturbation. And the design based on Single Lyapunov function is put forward in the form of LMI. And the stability bounds can also be determined.Differential-Algebraic Hybrid System (DAHS) is modeled whose subsystems are formulated by differential-algebraic equations besides pure differential equations. A framework of stability theory including the definition of stability and (globally) asymptotic stability was put forward based on the model of DAHS. And the sufficient conditions to test for stability and asymptotic stability were achieved in the case of arbitrary switching and slow switching by Single Lyapunov Function and Multiple Lyapunov Functions.The model of voltage stability is analyzed and abstracted to the model of Differential-Algebraic Hybrid System. So the judgment of voltage stability can be come down to the stability research of Differential-Algebraic Hybrid System. Using Single Lyapunov Function and Multiple Lyapunov Function, the stability problem of Differential-Algebraic Hybrid System is researched in the case of slow switching scenario. The sufficient conditions are derived to stabilized whole hybrid system by the switching laws put forward in this dissertation and used in the research of voltage stability. Multiple Lyapunov Function is better than Single Lyapunov Function in the analysis of hybrid system for the former is that each Lyapunov Function is active in an area rather than in the whole state space. The advantage simplifies the stability analysis. And the method can be used to analyze the influence of parameter varyingon the whole system. Therefore, when the method is used in the analysis of power system's voltage stability, it not only accounts for the validity of the switching law designed by the stability criterion put forward in this dissertation but also gives the stability margin of the system and judges the influence of the parameter varying on the whole system's stability.