Research On The Stability Of Sampling System Based On The Quasi-Lyapunov Functional Method

The sampled-data system plays an important role in networked control system,and has become an important branch in the field of modern digital control system.It has been widely valued and studied by many scholars.On the premise of ensuring the stability of sampling system,in order to reduce the computational burden,it is very important to increase the length of sampling interval.Therefore,it is of great significance to study the relationship between sampling interval and stability,that is,sampling dependent stability.On the other hand,in the actual industrial operation,there will inevitably be uncertainties in the system,which will have certain impact on the analysis and control of the system.Therefore,it is of great theoretical value and practical significance to study the sampling-dependent robust stability of uncertain sampled-data systems.In this paper,the stability of sampling system is further studied.Firstly,for deterministic sampling systems,by introducing a new Lyapunov-like functional and using advanced inequalities,the derivatives of the Lyapunov-like functional are estimated,and the stability conditions of sampling dependence with less conservativeness are obtained.Then,the condition is extended to convex polygon parameter uncertain sampling system,and a new condition for sampling-dependent robust stability of uncertain sampling system is obtained.Finally,the simulation is carried out with the LMI toolbox of MATLAB,and the validity of the method is verified.The main contents are as follows:In the first chapter,the background,structure,research status and research significance of the sampling system are introduced.Then,the state descriptions of the two systems studied in this paper are given: sampling control system and convex polygon parameter uncertain system.In the second chapter,Lyapunov stability theory is introduced,and the definitions and lemmas of asymptotic stability and exponential stability are given.Then the theory of linear matrix inequality is introduced,which provides the theoretical and simulation basis for the follow-up research.In the third chapter,the asymptotic stability of sampling system is studied by using Lyapunov-like functional method.By extending Lyapunov-like functional,the stability results with less conservativeness are obtained.Then,the stability results are extended to convex polygonal uncertain sampling systems,and a new robust asymptotic stability result is derived.The numerical simulation shows that the asymptotic stability results obtained in this chapter are less conservative than those obtained in some existing literatures.In the 4th chapter,the exponential stability of sampling system is studied by using Lyapunov-like functional method.The recently published results of asymptotic stability are extended to exponential stability,and the results of exponential stability with less conservativeness are obtained.Then,the results are transformed into convex polygon parameter uncertain systems by Schur complement lemma,and the new robust exponential stability results are obtained.The numerical simulation shows that the theorem in this chapter is a further extension of the related literature from asymptotic stability to exponential stability,and the results in this chapter are less conservative than those in the existing literature.The fifth chapter is the summary and prospect.The improvement and problems of this paper are explained respectively.