Sampled-Data Output Fee Dback Control For A Class Of Uncertain Nonlinear Systems

With the rapid development of digital computer and digital signal technology, sampled-data control systems, consisting of continuous-time plant and discrete-time controller, has been widely developed and applied in many areas. In the past few decades, fruitful results have been achieved on the research of the sampled-data control systems, but mostly focused on linear systems. Fewer results have been achieved on the sampled-data output feedback control of uncertain nonlinear systems, which is more complicated and worthy to be further investigated. In this paper, we mainly discuss sampled-data output feedback control of a class of uncertain nonlinear systems. The main contents are summarized as follows:(1) The problem of global sampled-data output feedback control is addressed for a class of feedforward nonlinear systems under a linear growth condition. By using a high-gain observer, a linear sampled-data output feedback control law is explicitly constructed. Combining the Lyapunov function with feedback domination approach, an explicit formula for the maximum allowable sampling period is obtained. It is shown that the closed-loop system can be globally stabilized by the proposed sampled-data output feedback controller with appropriately choosing the scaling gain and the sampling period.(2) The problem of global sampled-data output feedback practical tracking control is investigated for a class of uncertain nonlinear systems whose output functions are not precisely known. A new discrete-time observer is designed to estimate the unmeasurable states information at the sampling point. The sampled-data controller is obtained by discritizing the continuous-time controller constructed by using the backstepping method. By applying the Gronwall inequality and appropriately choosing the controller design parameters and the sampling period, it is proved that the proposed sampled-data controller guarantees all the signals of the closed-loop system to be bounded, and the tracking error converges to a small neighborhood of the origin in a finite time.(3) The problem of cooperative output synchronization of networked feedforward nonlinear systems is addressed via sampled-data output feedback control. A reduced-order sampled-data observer is constructed and a linear sampled-data controller is designed by using the Laplacian potential function and backstepping method. Combining graph theory with Lyapunov functional, an explicit formula for the sampling period can be obtained under the proposed controller with appropriate gains such that all the outputs of the agents in the network are synchronized eventually.