Stability Analysis Of Several Discrete Impulsive And Switched Systems

With the advancement and development of technology, the variouspower systems in reality become complex and networked, and some ofthem are usually nonlinear or uncertain, so it is difficult to describe themsimply, but it is extensive and far-reaching significance to research onstability analysis and control of power systems. Hybrid system is a typicalcomplex system with highly nonlinear, in the last ten years, stabilityanalysis for two typical hybrid system of impulse systems and switchingsystems has become a hot spot in the control community, and the methodof using hybrid control techniques (such as impulse and switchingcontrol) to research on networked control systems has begun, however,it needs more methods with systematic and effective to research on hybridcontrol.Firstly, the research status and development trend of hybrid systemsare reviewed, the basics of the stability which this article will be used toare introduced, and based on modern control theory, combined with theLyapunov method and linear matrix inequality (LMI) method,theproblem for the synchronization of discrete chaotic systems is analysed,several common synchronization control methods are listed, but theemphasis is the impulse synchronization control method. The discretechaotic system is used in secure communication, and the numericalsimulation by Matlab realize the synchronization of chaotic systems andthe encryption of signal.Secondly, we study the problem for hybrid control of discretedynamic network and the stability of discrete time-delay system by usingthe spectral radius and the average dwell time, based on this, and theproblem of the stability for discrete time-delay systems impulse networkis analysed in-depth. Mathematical proof of discrete time-delay systemstability under the conditions of the network in mathematics impulsecontrol is given and the simulation by matlab verifies the method.Finally, the impact of the impulse control and switching control for the system is analysed, and then the problem of stability for discretehybrid system under control and switching impulse control is studied,and the problem of stability and robust stability for several discreteimpulsive switched systems is discussed. The multiple Lyapunovfunctions is constructed for the system, the conditions that the system isasymptotically stable and exponentially stable under switching impulseconditions or switching rules are researched.In summary,this paper discusses some problems of the discretedynamic network hybrid control and its stability theory, which promotesstability of the the impulsive hybrid system and the development ofnetworked control systems, and it has some theoretical reference value.