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Hybrid dynamic system is composed of the interaction of discrete event systems and continuous variable systems constitute a complex system , the pulse mixing system is a hybrid system with impulsive phenomena . Hybrid system in hybrid automatic machine control , aircraft control , automatic train control , flexible manufacturing systems, network control systems and other practical problems in a wide range of applications . This paper studies a class of impulsive hybrid systems , its asymptotic stability, finite time stability discusses and design a mixed observer and the hybrid controller main summarized as follows: first , for a class of impulsive hybrid systems , the application of the backstepping method , designed a class of impulsive hybrid controller , and multiple Lyapunov function method to prove the stability of the closed-loop system , by numerical simulation of the control the effectiveness of the device for a class of impulsive hybrid systems , design mixed high gain observer , the observer mixed finite time observer and the finite time stability theory , by numerical simulation to verify the effectiveness Thirdly , for a class of impulsive hybrid systems , design a mixed observer and the mixed feedback controller , under the combined effect of the two closed-loop system to asymptotically stable , and construct a class of multiple Lyapunov functions , the application of multiple Lyapunov function method to prove the asymptotic stability of the closed-loop system , Finally, a numerical simulation to verify the effectiveness of the observer and controller .
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