Finite-time Control For A Class Of State Dependent Uncertain Systems

With the advancement of science and technology,various fields such as aviation,aerospace,and automobiles have been rapidly developed.In these industrial systems,high degree of integration and complication has become a development trend.However,there are often various unknown uncertainties in these complex systems.The existence of uncertainty is likely to cause the system's performance to deviate from the ideal expectations,or even unable to work.Therefore,before the analysis of various types of systems,a model must be established.Uncertainty is an important factor to consider.The actual industrial system is mostly composed of mechanical and electronic circuit systems.There are some non-linear components in such systems,such as tunnel diodes.This kind of uncertainty is rather special and depends mainly on the system state.Therefore,it is meaningful to study this type of uncertainty system.In addition,the stability of the system is usually the main focus of system research,and most of the studies are asymptotically stable.However,some applications have higher transient requirements on the system.The system state reaches an ideal state within a limited time.The system needs to have finite time stability.Therefore,it is of practical significance to study the finite-time control of such systems.At the same time,with the development of digital technology,most systems currently communicate through digital networks.Therefore,research on such network control systems becomes very important.This paper will study the finite time control of a class of state-dependent uncertain systems.This paper focuses on the state-independent uncertain system.Its main description method is convex polyhedron.We will give a finite-time boundedness theorem and a kind of controller design method.And the system has H? performance indicators.The method of this paper is to construct a reasonable quadratic Lyapunov function,combined with the finite-time stability decision theorem and the Lyapunov stability theory.At the same time,this paper will give the linear matrix inequalities that can be solved.Considering the network transmission delay the bandwidth-constrained problem in the networked control system,a model description of the system is given.This article will introduce a periodic event-triggered mechanism into the system to save communication resources to solve the bandwidth limitation problem.The method of this paper is to give a reasonable Lyapunov-Krasovskii function,then use a similar analysis method.Finally,the controller design method is given to make the system meet the condition of the finite-time boundedness and has H? performance index.Finally,the theorem is applied to the actual system simulation.For networked control systems,it is crucial to obtain continuous status information.Therefore,a mixed event-triggered mechanism is proposed in this paper to make up for the limitation that the periodic event-triggered mechanism only obtains the status information at the sampling time.In this paper,after introducing the trigger mechanism,a kind of switching method is used to convert the system into a class of time-delay switching system.The corresponding decision theorem about the finite-time stability and boundedness and controller design method are given.Finally,the tunnel diode circuit is used to verify the accuracy of the theorem.