Research On The Stability For A Class Of Distributed Parameter Hybrid Systems

By semigroup theory and general orthogonal polynomials (GOP), the stability of a class of distributed parameter hybrid systems (DPHS) and a class of distributed parameter switched systems (DPSS), the stabilization for a class of DPSS and the approximate analysis for distributed parameter control systems were discussed in this dissertation.The chief work and innovation in this paper are as follows:Firstly, a general model for DPHS was established and it's stability was analyzed using the quintuple analysis method of hybrid dynamical systems and it's relative theory.Secondly, the stability analysis for DPSS was given. The stability DPSS include exponential stable sub-systems was discussed, and the state feedback stabilization is also presented. In the next place, an observer is designed for a class of DPSS whose sub-system is linear, and a sufficient condition for the stabilization of closed-loop system is also presented. Based on these, a switching strategy and sub-controller, which use the observer value, are designed to guarantee the closed-loop system is exponentially asymptotically stable. The switching strategy and sub-controllers can also guarantee the closed-loop system is exponentially asymptotically stable even if the switching interval time is constrained.In addition, in response to widespread pulse effect in DPSS, a model of distribution parameters impulsive switched systems (DPISS) was given. The stability of DPISS was also analyzed. Meanwhile, for DPISS, including the nonlinear and uncertain item, their stability was also studied.Finally, the finite-dimensional approximation for distributed parameter systems was studied. The algorithms and approximate rules of GOP were given and convergence was proved on space L~2[a,b]. The optimal approximate control and predictive control for distributed parameter systems have been studied via GOP and the simulation example was given to demonstrate the effectiveness of this method. The switching law is difficult to be obtained for simulation process of DPSS, but the approximate switching law is easy to be obtained via this method and have the simulation process of DPSS finished. An effective way for simulation of DPSS was presented by this method.Besides, simulations are made for main results. Simulation results show the effectiveness of the proposed approaches.