Stability Analysis Of Linear Sampled-data Systems Based On Time-varying Lyapunov-Krasovskii Functional

With the development of computer technology,digital technology and sensor technol-ogy have been facilitated the widespread use of sampled-data control in social,economic,and industrial fields.Therefore,sampled-data systems have been widely used,and re-search on the theory of sampled-data systems has great practicality.For the hybrid of the sampled-data systems,the existence of problems such as network-induced delays,packet-dropouts,time-varying sampling period,the uncertainty and external disturbance factors.This makes the stability analysis and control design of the sampled-data systems are more complex.Thus,a few research results on sampled-data systems are reported and there are still many problems to be solved.However,variable sampling is a key factor to affect the stability of sampled-data systems.Therefore,we will further study the stability anal-ysis problem of linear sampled-data systems with a time-varying sampling period,and describe the relationship between the stability of systems and the sampling period.The main contributions are as follows:Chapter 1 is the preface,which summarizes the sampled-data systems and the linear sampled-data systems with time-varying sampling period,and the main contents of this paper are briefly introduced.Chapter 2 studies the problem of asymptotically stability analysis for a linear sampled-data systems with time-varying sampling period.This paper first models such a sampled-date input system as a continuous one,where the control input has a piecewise-continuous delay.Then,sufficient conditions in terms of linear matrix inequalities are derived by constructing a class of time-varying Lyapunov functional to achieve the stability of the closed-loop time-delay system.The feature of the constructed Lyapunov functionals is discontinuous at sampling time,but its decrease of such Lyapunov functional at sampling time is guaranteed by construction.Finally,an example is given to show the effectiveness of the proposed method.Chapter 3 studies the problem of exponential stability analysis of a linear sampled-data systems with time-varying sampling period.This paper first models such a sampled-date input system as a continuous one,where the control input has a piecewise-continuous delay.Then,sufficient conditions in terms of linear matrix inequalities are derived by con-structing a class of time-varying Lyapunov functional to achieve the exponential stability of the closed-loop time-delay system.The feature of the constructed Lyapunov function-als is discontinuous at sampling time,but its decrease of such Lyapunov functional at sampling time is guaranteed by construction.Finally,the proposed stability results are less conservative than the existing ones.The conclusions and perspectives end the dissertation.