| The optimal switching law of switched systems is researched in this article. As an important class of hybrid dynamical systems, the switched system is composed of a family of continuous-time or discrete-time subsystems and a rule orchestrating the switching among the subsystems. Due to the switching signal, its dynamical performance becomes very complicated. Hence, it is very important to choose a property switching law in the practical production.This dissertation investigates how to choose a proper switching law from switching time for the linear switched systems. The main work incules the analysis of the optimal switching laws of impulsive swithed systems and the research on the optimal switching laws based on norm and convergence path, the choosing of switching laws. The main contributions of the research work presented in this dissertation are as follows:(1) The optimal switching law is discussed for the linear impulsive switched systems. Firstly, asymptotically stable value range of the switching law is obtained based on the constraint condition of matrix pencil for the linear impulsive switched system. Secondly, different running results of system are got because of the choosing of switching law, in the asymptotically stable convergence process of switched system. Then, the analysis method of optimal switching law based on the norm is present in the view of the gradually decreased norm value of the state points after the switching. Finally, instance simulation verify the effectiveness of this method.(2) The optimal switching law of switching systems based on the convergence of the optimal switching path in the asymptotic stability conditions is studied for a class of periodic switched linear impulsive switched systems. The analysis of the optimal switching based on the convergence route is present from asymptotically stable convergence process the minimum angle of path of converge operation. The simulation example, verify the correctness and validity of the design method. |
PDF Full Text Request