A Kind Of Multirate Nonlinear Sampled-data Control Systems

In this paper, we mainly study a kind of multirate nonlinear sampled-data control systems, and discuss the stability properties of its solution while its sampler produces quantization during sampling. Here we use two different ways, CDT and DTD, to design the controller, and take the sampling state as the initial state for the process of Euler iterative approximation, which adequately consider the effect of quanzation. Then we take the approximate state instead of the state of the controllers, and use the modified controllers to stabilize the closed-loop sampled-data control systems and the corresponding exact discrete systems of the continuous controlled system. We can obtain the solution of the systems is practicable stability under the condition that approximate and sampling quantization are restricted (Theorem 2.2.1, Theorem 2.2.2 and Theorem 3.2.1).The paper is organized as follows: In the first chapter, we introduce a background question and establish the mathematic model; the controllers based on the continuous and discrete time systems are designed, which is the base of analyzing the stability of the nonlinear sampled-data control systems with quantization respectively in the second and third chapter. In the fourth chapter, we mainly verify the theorem and process the calculator emulation with a material case. In the fifth chapter, I summarize the idea and the question, which encountered during the study of the multirate nonlinear sampled-data control systems, and view the possible trends in the study of this kind systems in the future. At last, I list the references and express my great appreciation to every one who helps me.