Uncertain Sampling System Depends On The Robust Stability Of Sampling

The sampled-data system plays an important role in the network control system.It has become an important branch of modern digital control system.And it is widely valued and studied by many scholars.Under the premise that the sampled-data system is stable,to reduce the computational burden and improve the data transmission rate,increasing the length of the sampling interval is critical.On the other hand,in the actual industrial operation,the system will inevitably have an uncertain factor,which will bring us some influence on the analysis and control of the system.Therefore,it is of great theoretical value and practical significance to study the robust stability of uncertain sampled-data system.The stability of the sampled-data system is further studied in this paper.The stability conditions of deterministic sampled-data control system are obtained by introducing a new Lyapunov-like functional and combining with the advanced inequality to estimate his derivative.Then the stability conditions are generalized to study the robust stability conditions of the sampled-data systems with polytopic uncertainties.And the effectiveness of these stability conditions can be verified by the LMI toolbox.The main contents of this article are as follows:Chapter 1 briefly introduces the background,status and significance of the sampled-data control system,and points out the problems to be studied in this paper.Chapter 2 lists some of the theoretical knowledge and important lemma needed in this article,which provides theoretical basis for the following research.Chapter 3 researches the stability of the deterministic sampled-data system.With the introduction of sampled-data system at the right end of the sampling interval and the cross-term with the state integral over the integral interval of?t _k,t?.Hence,a new Lyapunov-like functional is constructed.Then by taking advantages of the improved Wirtinger integral inequality and the Jensen inequality,a new theorem is obtained.Then transform the results by the complementary lemma of Schur.A new method is derived for the robust exponential stability of uncertain sampled-data system.The final numerical simulations illustrate that the methods of this chapter do have the fewer conservative results than some existing literature.Chapter 4 is based on the chapter 3 using the information of the sampled-data system in the interval(t,t_k?10?1)and?t _k,t?.Construct a new Lyapunov-like functional and obtain the new methods of the improved asymptotic stability and the robust stability of the sampled-data systems with polytopic uncertainties.Finally,the simulative examples are presented to verify the effectiveness of above methods when compared with the corresponding asymptotic stability of chapter 3 and some of the existing literature.Chapter 5 is to summarize the research content of this article,and the future research is also discussed.