Sampled-data Control For Two Classes Of Continuous-time Systems Under Different Sampling Schemes

Recently, with the rapid development of digital measurement technology and intelligent instrument, many control systems consist of continuous-time plants and discrete-time controllers (which can be implemented by digital computer, etc.), that is sampled-data control systems. In such systems, adopting different sampling schemes may affect the stability and performance of the systems directly. So it is a significant issue to investigate the sampled-data control for sampled-data control systems. On the other hand, many plants in industry have severe nonlinear characteristics. T-S fuzzy models are shown to be universal function approximators in the sense that they are able to approximate any smooth nonlinear function to any degree of accuracy in any convex compact region. Hence, it is important to investigate the stochastic sampled-data control for nonlinear systems based on T-S fuzzy models both in theory and practice.The main results in the dissertation are as follows.In chapter 1, the significance of this thesis is introduced in both theory and application. And the research situation at home and abroad is recalled.In chapter 2, the problem of stochastic sampled-data control for a class of nonlinear continuous-time systems is investigated. For the sake of presentation simplicity, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By using the input delay approach and the T-S fuzzy system method, a class of nonlinear continuous- time systems with stochastic sampling is transformed into a continuous-time T-S fuzzy system with time-varying delays and the stochastic parameters. Based on Lyapunov stability theory, a mean square asymptotic stability condition for the closed-loop T-S fuzzy system is proposed. Furthermore, the controller design method is given in terms of LMI. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.In chapter 3, the thesis investigates the exponential stabilization problem of linear systems under different sampling period of state sub-vectors. Since the sensors used for sampling different state variables are different and their sampling periods may be different, the state variables are reclassified in order that the controller uses the real-time sampling information and the state variables classified in the identical sub-vector are sampled by one same sampling period. Such sampling scheme is called the classified-states multi-rate sampling (CSMS) in this paper. By the input delay approach, the sampled-data control system with CSMS is modeled as a switched system with time-varying delays. Based on the switched system approach and Lyapunov stability theory, an exponential stability condition for such system is proposed, and the design of the corresponding switched-sampling controller is presented by solving a set of linear matrix inequalities (LMIs). Finally, to demonstrate the merits of the proposed approach, we compare it with the controller design method under single rate sampling of all state variables for the sampled-data control of the rotating base pendulum and closed-loop automobile driving.In chapter 4, the main results of the thesis are concluded, and some research directions on sampled-data control in future are proposed.