The Stabilization Of Sampled-Data Systems With Time-Varying Sampling Periods

There are many sampled-data systems in life. You can find it from daily life to science research. So the study of sampled-data systems becomes more popular in recent years. Though it has been several decades since people study them, we have obtained many results. Most of them are concerned with the stability analysis and stabilization of sampled-data systems with fixed-sampling periods or multirate-sampling periods which have sound theories. While the research of sampled-data systems with time-varying sampling periods is very rare. And the linear principle is used in these articles.For the stability analysis and stabilization of sampled-data systems, there are two tools following: Lyapunov function and K.-L function. We use the Lyapunov function to show the stabilization of sampled-data systems with time-varying sampling periods. In this paper, we study the stabilization of sampled-data systems with time-varying sampling periods below:x(t) = f(x(t),α(x(ι_k),T_k)) t∈[t_kkt_k+1) ∨k∈N. Some results will be given in this thesis:First proving Lyapunov theories of system x(t_k+1) = F(x(t_k ),T_k) (T_k = t_k+1-t_k) under the condition that the system is exponentially stable and making foundation for the stability analysis of sampled-data systems with time-varying sampling periods. Second giving sufficient conditions for exponential stability of sampled-data systems under the condition that its exact discrete-time model is exponentially stable and showing the design of digital controller when the sampling periods T_k- T. Last showing that the sampled-data system is practically exponentially stable if it satisfies certain condition and its approximate discrete-time model is exponentially stable.We avoid the use of linear principle and expand the valid scale of results.